Pub Date : 2025-12-01Epub Date: 2025-11-05DOI: 10.1016/j.jpaa.2025.108125
Pedro Macias Marques , Rosa M. Miró-Roig , Josep Pérez
In this paper, we compute all possible Jordan types of linear forms in any full Perazzo algebra. In some cases we are also able to compute the corresponding Jordan degree-type, which is a finer invariant.
{"title":"Jordan type of full Perazzo algebras","authors":"Pedro Macias Marques , Rosa M. Miró-Roig , Josep Pérez","doi":"10.1016/j.jpaa.2025.108125","DOIUrl":"10.1016/j.jpaa.2025.108125","url":null,"abstract":"<div><div>In this paper, we compute all possible Jordan types of linear forms in any full Perazzo algebra. In some cases we are also able to compute the corresponding Jordan degree-type, which is a finer invariant.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108125"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-10-30DOI: 10.1016/j.jpaa.2025.108120
Fulin Chen , Xin Huang , Fei Kong , Shaobin Tan
In this paper, we associate the quantum toroidal algebra of type with quantum vertex algebra through equivariant ϕ-coordinated quasi modules. More precisely, for every , by deforming the universal affine vertex algebra of , we construct an ħ-adic quantum -vertex algebra . Then we prove that the category of restricted -modules of level ℓ is canonically isomorphic to that of equivariant ϕ-coordinated quasi -modules.
{"title":"Quantum vertex algebra associated to quantum toroidal glN","authors":"Fulin Chen , Xin Huang , Fei Kong , Shaobin Tan","doi":"10.1016/j.jpaa.2025.108120","DOIUrl":"10.1016/j.jpaa.2025.108120","url":null,"abstract":"<div><div>In this paper, we associate the quantum toroidal algebra <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> of type <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> with quantum vertex algebra through equivariant <em>ϕ</em>-coordinated quasi modules. More precisely, for every <span><math><mi>ℓ</mi><mo>∈</mo><mi>C</mi></math></span>, by deforming the universal affine vertex algebra of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, we construct an <em>ħ</em>-adic quantum <span><math><mi>Z</mi></math></span>-vertex algebra <span><math><msub><mrow><mi>V</mi></mrow><mrow><msub><mrow><mover><mrow><mi>sl</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>∞</mo></mrow></msub><mo>,</mo><mi>ħ</mi></mrow></msub><mo>(</mo><mi>ℓ</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>. Then we prove that the category of restricted <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span>-modules of level <em>ℓ</em> is canonically isomorphic to that of equivariant <em>ϕ</em>-coordinated quasi <span><math><msub><mrow><mi>V</mi></mrow><mrow><msub><mrow><mover><mrow><mi>sl</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>∞</mo></mrow></msub><mo>,</mo><mi>ħ</mi></mrow></msub><mo>(</mo><mi>ℓ</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>-modules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108120"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-12-05DOI: 10.1016/j.jpaa.2025.108146
Yilin Wu , Jinyi Xu , Guodong Zhou
Several GAGA-type results for singularity categories are presented. Firstly, as an easy consequence of Serre's GAGA theorem, we show that for a complex projective variety, its singularity category is naturally equivalent to that of its analytification.
Secondly, we introduce the torsion singularity category of a formal scheme. Under Orlov's (ELF) condition, we prove that for the formal completion of a Noetherian scheme along a closed subset, its torsion singularity category is equivalent to the singularity category of the original scheme, with support in the closed subset.
Lastly, using the Artin Approximation Theorem and the result above, we provide an alternative proof of a result of Orlov. Namely, for a Noetherian local ring with an isolated singularity, its singularity category is equivalent (up to direct summands) to that of its Henselization, which in turn is equivalent to that of its completion.
{"title":"GAGA type results for singularity categories","authors":"Yilin Wu , Jinyi Xu , Guodong Zhou","doi":"10.1016/j.jpaa.2025.108146","DOIUrl":"10.1016/j.jpaa.2025.108146","url":null,"abstract":"<div><div>Several GAGA-type results for singularity categories are presented. Firstly, as an easy consequence of Serre's GAGA theorem, we show that for a complex projective variety, its singularity category is naturally equivalent to that of its analytification.</div><div>Secondly, we introduce the torsion singularity category of a formal scheme. Under Orlov's (ELF) condition, we prove that for the formal completion of a Noetherian scheme along a closed subset, its torsion singularity category is equivalent to the singularity category of the original scheme, with support in the closed subset.</div><div>Lastly, using the Artin Approximation Theorem and the result above, we provide an alternative proof of a result of Orlov. Namely, for a Noetherian local ring with an isolated singularity, its singularity category is equivalent (up to direct summands) to that of its Henselization, which in turn is equivalent to that of its completion.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108146"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-12-03DOI: 10.1016/j.jpaa.2025.108142
A.A. Ambily, H. Sugilesh
We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring , over a commutative ring R in which 2 is invertible, as a product of an orthogonal matrix with entries in R and an elementary orthogonal matrix with entries from .
{"title":"Horrocks' theorem for odd orthogonal groups","authors":"A.A. Ambily, H. Sugilesh","doi":"10.1016/j.jpaa.2025.108142","DOIUrl":"10.1016/j.jpaa.2025.108142","url":null,"abstract":"<div><div>We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring <span><math><mi>R</mi><mo>[</mo><mi>X</mi><mo>]</mo></math></span>, over a commutative ring <em>R</em> in which 2 is invertible, as a product of an orthogonal matrix with entries in <em>R</em> and an elementary orthogonal matrix with entries from <span><math><mi>R</mi><mo>[</mo><mi>X</mi><mo>]</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108142"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-12-02DOI: 10.1016/j.jpaa.2025.108139
Jiří Adámek
Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms).
{"title":"Which categories are varieties of quantitative algebras?","authors":"Jiří Adámek","doi":"10.1016/j.jpaa.2025.108139","DOIUrl":"10.1016/j.jpaa.2025.108139","url":null,"abstract":"<div><div>Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms).</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108139"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-12-02DOI: 10.1016/j.jpaa.2025.108137
Anna Laura Suarez
<div><div>We introduce a pointfree version of Raney duality. Our objects are <em>Raney extensions</em> of frames, pairs <span><math><mo>(</mo><mi>L</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span> where <em>C</em> is a coframe and <span><math><mi>L</mi><mo>⊆</mo><mi>C</mi></math></span> is a subframe that meet-generates it and whose embedding preserves strongly exact meets. We show that there is a dual adjunction between <strong>Raney</strong> and <strong>Top</strong>, with all <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> spaces as fixpoints, assigning to a space <em>X</em> the pair <span><math><mo>(</mo><mi>Ω</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math></span>, with <span><math><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> are the intersections of open sets. We show that for every Raney extension <span><math><mo>(</mo><mi>L</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span> there are subcolocale inclusions <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mi>L</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>p</mi></mrow></msup><mo>⊆</mo><mi>C</mi><mo>⊆</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span> where <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span> is the coframe of fitted sublocales and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span> is the frame of joins of closed sublocales. We thus exhibit a symmetry between these two well-studied structures in pointfree topology. The spectra of these are, respectively, the classical spectrum <span><math><mrow><mi>pt</mi></mrow><mo>(</mo><mi>L</mi><mo>)</mo></math></span> of the underlying frame and its <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> spectrum <span><math><msub><mrow><mi>pt</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span>. This confirms the view advanced in <span><span>[9]</span></span> that sobriety and the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> property are mirror images of each other, and suggests that the symmetry above is a pointfree view of it. All Raney extensions satisfy some variation of the properties <em>density</em> and <em>compactness</em> from the theory of canonical extensions. We characterize sobriety, the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, and the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> axioms in terms of density and compactness of <span><math><mo>(</mo><mi>Ω</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math></span>. We characterize frame morphisms <span><math><mi>f</mi><mo>
{"title":"Raney extensions: A pointfree theory of T0 spaces based on canonical extension","authors":"Anna Laura Suarez","doi":"10.1016/j.jpaa.2025.108137","DOIUrl":"10.1016/j.jpaa.2025.108137","url":null,"abstract":"<div><div>We introduce a pointfree version of Raney duality. Our objects are <em>Raney extensions</em> of frames, pairs <span><math><mo>(</mo><mi>L</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span> where <em>C</em> is a coframe and <span><math><mi>L</mi><mo>⊆</mo><mi>C</mi></math></span> is a subframe that meet-generates it and whose embedding preserves strongly exact meets. We show that there is a dual adjunction between <strong>Raney</strong> and <strong>Top</strong>, with all <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> spaces as fixpoints, assigning to a space <em>X</em> the pair <span><math><mo>(</mo><mi>Ω</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math></span>, with <span><math><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> are the intersections of open sets. We show that for every Raney extension <span><math><mo>(</mo><mi>L</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></span> there are subcolocale inclusions <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><msup><mrow><mo>(</mo><mi>L</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>p</mi></mrow></msup><mo>⊆</mo><mi>C</mi><mo>⊆</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span> where <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>o</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span> is the coframe of fitted sublocales and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span> is the frame of joins of closed sublocales. We thus exhibit a symmetry between these two well-studied structures in pointfree topology. The spectra of these are, respectively, the classical spectrum <span><math><mrow><mi>pt</mi></mrow><mo>(</mo><mi>L</mi><mo>)</mo></math></span> of the underlying frame and its <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> spectrum <span><math><msub><mrow><mi>pt</mi></mrow><mrow><mi>D</mi></mrow></msub><mo>(</mo><mi>L</mi><mo>)</mo></math></span>. This confirms the view advanced in <span><span>[9]</span></span> that sobriety and the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> property are mirror images of each other, and suggests that the symmetry above is a pointfree view of it. All Raney extensions satisfy some variation of the properties <em>density</em> and <em>compactness</em> from the theory of canonical extensions. We characterize sobriety, the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, and the <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> axioms in terms of density and compactness of <span><math><mo>(</mo><mi>Ω</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>,</mo><mi>U</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></math></span>. We characterize frame morphisms <span><math><mi>f</mi><mo>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108137"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-11-19DOI: 10.1016/j.jpaa.2025.108135
Rinat Kashaev , Vladimir Mangazeev
We show that the exterior algebra of a vector space V of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis.
A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang–Baxter equation. These solutions are conjectured to give rise to the two-variable Links–Gould polynomial invariants associated with the super-quantum group , where . We support this conjecture through computations for small values of N.
{"title":"On braided Hopf structures on exterior algebras","authors":"Rinat Kashaev , Vladimir Mangazeev","doi":"10.1016/j.jpaa.2025.108135","DOIUrl":"10.1016/j.jpaa.2025.108135","url":null,"abstract":"<div><div>We show that the exterior algebra of a vector space <em>V</em> of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis.</div><div>A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang–Baxter equation. These solutions are conjectured to give rise to the two-variable Links–Gould polynomial invariants associated with the super-quantum group <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mrow><mi>gl</mi></mrow><mo>(</mo><mi>N</mi><mo>|</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span>, where <span><math><mi>N</mi><mo>=</mo><mi>dim</mi><mo></mo><mo>(</mo><mi>V</mi><mo>)</mo></math></span>. We support this conjecture through computations for small values of <em>N</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108135"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-01Epub Date: 2025-12-02DOI: 10.1016/j.jpaa.2025.108140
Radha Kessar , Jason Semeraro , Patrick Serwene , İpek Tuvay
We prove that the Parker–Semeraro systems satisfy six of the nine Kessar–Linckelmann–Lynd–Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal 3-block of , the principal 5-blocks of HN, BM, , Ly, the principal 7-block of M, and the principal p-blocks of for .
{"title":"Weight conjectures for Parker–Semeraro fusion systems","authors":"Radha Kessar , Jason Semeraro , Patrick Serwene , İpek Tuvay","doi":"10.1016/j.jpaa.2025.108140","DOIUrl":"10.1016/j.jpaa.2025.108140","url":null,"abstract":"<div><div>We prove that the Parker–Semeraro systems satisfy six of the nine Kessar–Linckelmann–Lynd–Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal 3-block of <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></span>, the principal 5-blocks of <em>HN</em>, <em>BM</em>, <span><math><mrow><mi>Aut</mi></mrow><mo>(</mo><mi>H</mi><mi>N</mi><mo>)</mo></math></span>, <em>Ly</em>, the principal 7-block of <em>M</em>, and the principal <em>p</em>-blocks of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>p</mi><mo>)</mo></math></span> for <span><math><mi>p</mi><mo>≥</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108140"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-19DOI: 10.1016/j.jpaa.2025.108096
Yanjie Li , Shizhuo Zhang
Let be 2g dimensional quadrics in and let Y be the smooth intersection . We associate the linear subspaces in Y with vector bundles on the hyperelliptic curve C of genus g via categorical methods. As an application, we give a different proof of the classification of line bundles and stable bundles of rank 2 on hyperelliptic curves given by Desale and Ramanan. When , we show that the projection functor induces a closed embedding into the moduli space of stable bundles on C of rank 4 of fixed determinant.
{"title":"Linear subspaces of the intersection of two quadrics via Kuznetsov component","authors":"Yanjie Li , Shizhuo Zhang","doi":"10.1016/j.jpaa.2025.108096","DOIUrl":"10.1016/j.jpaa.2025.108096","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> be 2<em>g</em> dimensional quadrics in <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn><mi>g</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> and let <em>Y</em> be the smooth intersection <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>∩</mo><msub><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We associate the linear subspaces in <em>Y</em> with vector bundles on the hyperelliptic curve <em>C</em> of genus <em>g</em> via categorical methods. As an application, we give a different proof of the classification of line bundles and stable bundles of rank 2 on hyperelliptic curves given by Desale and Ramanan. When <span><math><mi>g</mi><mo>=</mo><mn>3</mn></math></span>, we show that the projection functor induces a closed embedding <span><math><mi>α</mi><mo>:</mo><mi>Y</mi><mo>→</mo><mi>S</mi><msubsup><mrow><mi>U</mi></mrow><mrow><mi>C</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mo>(</mo><mn>4</mn><mo>,</mo><mi>h</mi><mo>)</mo></math></span> into the moduli space of stable bundles on <em>C</em> of rank 4 of fixed determinant.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108096"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01Epub Date: 2025-09-19DOI: 10.1016/j.jpaa.2025.108098
Kamal Aziziheris , Necat Gorentas , Zinah Naser Sulaiman
Let be the average degree of irreducible characters of G with odd degree. It has been proved that if , then G is a solvable group. On the other hand, let be the average degree of linear characters and irreducible characters of G with even degree. It has been shown that if , then G is a solvable group. In this paper, we improve these bounds and we show that if G is a finite group with , then either G is a solvable group or G has a chief factor isomorphic to . Also, we prove that if G is a finite group with , then either G is a solvable group or all minimal normal subgroups of G are abelian or isomorphic to . Clearly, these bounds are the best.
{"title":"On the average degree of characters with odd or even degrees","authors":"Kamal Aziziheris , Necat Gorentas , Zinah Naser Sulaiman","doi":"10.1016/j.jpaa.2025.108098","DOIUrl":"10.1016/j.jpaa.2025.108098","url":null,"abstract":"<div><div>Let <span><math><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the average degree of irreducible characters of <em>G</em> with odd degree. It has been proved that if <span><math><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo><</mo><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>3</mn></math></span>, then <em>G</em> is a solvable group. On the other hand, let <span><math><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> be the average degree of linear characters and irreducible characters of <em>G</em> with even degree. It has been shown that if <span><math><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo><</mo><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub><mo>)</mo><mo>=</mo><mn>5</mn><mo>/</mo><mn>2</mn></math></span>, then <em>G</em> is a solvable group. In this paper, we improve these bounds and we show that if <em>G</em> is a finite group with <span><math><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo><</mo><msub><mrow><mi>acd</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mrow><mi>PSL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>7</mn><mo>/</mo><mn>2</mn></math></span>, then either <em>G</em> is a solvable group or <em>G</em> has a chief factor isomorphic to <span><math><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub></math></span>. Also, we prove that if <em>G</em> is a finite group with <span><math><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo><</mo><msub><mrow><mi>acd</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mrow><mi>PSL</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>)</mo><mo>=</mo><mn>9</mn><mo>/</mo><mn>2</mn></math></span>, then either <em>G</em> is a solvable group or all minimal normal subgroups of <em>G</em> are abelian or isomorphic to <span><math><msub><mrow><mtext>A</mtext></mrow><mrow><mn>5</mn></mrow></msub></math></span>. Clearly, these bounds are the best.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 11","pages":"Article 108098"},"PeriodicalIF":0.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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