Pub Date : 2025-12-01DOI: 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 : 2025-12-01DOI: 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 : 2025-12-01DOI: 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 : 2025-11-10DOI: 10.1016/j.jpaa.2025.108128
Agata Smoktunowicz
This paper presents an extension of the classical method [1] for associating groups to pre-Lie rings. This enhancement will hopefully help us to better understand an object used to investigate set-theoretic solutions of the Yang-Baxter equation and Hopf-Galois extensions called a brace. We also show that some classes of braces of cardinality with p prime and n larger than p can be obtained with our extension.
{"title":"An extension of the group of flows method for finite pre-Lie rings","authors":"Agata Smoktunowicz","doi":"10.1016/j.jpaa.2025.108128","DOIUrl":"10.1016/j.jpaa.2025.108128","url":null,"abstract":"<div><div>This paper presents an extension of the classical method <span><span>[1]</span></span> for associating groups to pre-Lie rings. This enhancement will hopefully help us to better understand an object used to investigate set-theoretic solutions of the Yang-Baxter equation and Hopf-Galois extensions called a brace. We also show that some classes of braces of cardinality <span><math><msup><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with <em>p</em> prime and <em>n</em> larger than <em>p</em> can be obtained with our extension.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108128"},"PeriodicalIF":0.8,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528932","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 : 2025-11-10DOI: 10.1016/j.jpaa.2025.108129
Lucas Hamada, Kazuki Kato, Ryo Komiya
This paper investigates a Tate algebra version of the Jacobian conjecture, referred to as the Tate-Jacobian conjecture, for commutative rings R equipped with an I-adic topology. We show that if the I-adic topology on R is Hausdorff and is a subring of a -algebra, then the Tate-Jacobian conjecture is equivalent to the Jacobian conjecture. Conversely, if has positive characteristic, the Tate-Jacobian conjecture fails. Furthermore, we establish that the Jacobian conjecture for is equivalent to the following statement: for all but finitely many primes p, the inverse of a polynomial map over whose Jacobian determinant is an element of lies in the Tate algebra over .
{"title":"A Tate algebra version of the Jacobian conjecture","authors":"Lucas Hamada, Kazuki Kato, Ryo Komiya","doi":"10.1016/j.jpaa.2025.108129","DOIUrl":"10.1016/j.jpaa.2025.108129","url":null,"abstract":"<div><div>This paper investigates a Tate algebra version of the Jacobian conjecture, referred to as <em>the Tate-Jacobian conjecture</em>, for commutative rings <em>R</em> equipped with an <em>I</em>-adic topology. We show that if the <em>I</em>-adic topology on <em>R</em> is Hausdorff and <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> is a subring of a <span><math><mi>Q</mi></math></span>-algebra, then the Tate-Jacobian conjecture is equivalent to the Jacobian conjecture. Conversely, if <span><math><mi>R</mi><mo>/</mo><mi>I</mi></math></span> has positive characteristic, the Tate-Jacobian conjecture fails. Furthermore, we establish that the Jacobian conjecture for <span><math><mi>C</mi></math></span> is equivalent to the following statement: for all but finitely many primes <em>p</em>, the inverse of a polynomial map over <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> whose Jacobian determinant is an element of <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>×</mo></mrow></msubsup></math></span> lies in the Tate algebra over <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108129"},"PeriodicalIF":0.8,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528933","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 : 2025-11-10DOI: 10.1016/j.jpaa.2025.108130
Abhishek Das , Santosha Pattanayak
We consider typical finite dimensional complex irreducible representations of a basic classical Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for , , and under some assumptions. This result is a Lie superalgebra analogue of Rajan's fundamental result [10] on unique factorization of tensor products for finite dimensional complex simple Lie algebras.
{"title":"On tensor products of representations of Lie superalgebras","authors":"Abhishek Das , Santosha Pattanayak","doi":"10.1016/j.jpaa.2025.108130","DOIUrl":"10.1016/j.jpaa.2025.108130","url":null,"abstract":"<div><div>We consider typical finite dimensional complex irreducible representations of a basic classical Lie superalgebra, and give a sufficient condition on when unique factorization of finite tensor products of such representations hold. We also prove unique factorization of tensor products of singly atypical finite dimensional irreducible modules for <span><math><mrow><mi>sl</mi></mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><mrow><mi>osp</mi></mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>)</mo></math></span>, <span><math><mi>G</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span> and <span><math><mi>F</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></span> under some assumptions. This result is a Lie superalgebra analogue of Rajan's fundamental result <span><span>[10]</span></span> on unique factorization of tensor products for finite dimensional complex simple Lie algebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108130"},"PeriodicalIF":0.8,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579725","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 : 2025-11-07DOI: 10.1016/j.jpaa.2025.108127
Dmitriy Voloshyn
We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of one variety onto another. In particular, we develop tools for proving that an upper cluster algebra equals the given commutative ring.
{"title":"Starfish lemma via birational quasi-isomorphisms","authors":"Dmitriy Voloshyn","doi":"10.1016/j.jpaa.2025.108127","DOIUrl":"10.1016/j.jpaa.2025.108127","url":null,"abstract":"<div><div>We study birational quasi-isomorphisms between normal Noetherian domains endowed with cluster structures of geometric type. We prove an analogue of the Starfish lemma that allows one to transfer various cluster and algebraic properties of one variety onto another. In particular, we develop tools for proving that an upper cluster algebra equals the given commutative ring.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108127"},"PeriodicalIF":0.8,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528934","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 : 2025-11-05DOI: 10.1016/j.jpaa.2025.108126
Hongda Lin , Honglian Zhang
In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra . First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra , explicitly constructing its current generators and defining relations. A key innovation is the construction of a Poincaré-Birkhoff-Witt (PBW) basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode.
{"title":"Drinfeld super Yangian of the exceptional Lie superalgebra D(2,1;λ)","authors":"Hongda Lin , Honglian Zhang","doi":"10.1016/j.jpaa.2025.108126","DOIUrl":"10.1016/j.jpaa.2025.108126","url":null,"abstract":"<div><div>In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra <span><math><mi>D</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>;</mo><mi>λ</mi><mo>)</mo></math></span>. First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra <span><math><mi>D</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>;</mo><mi>λ</mi><mo>)</mo></math></span>, explicitly constructing its current generators and defining relations. A key innovation is the construction of a Poincaré-Birkhoff-Witt (PBW) basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108126"},"PeriodicalIF":0.8,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475355","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 : 2025-11-05DOI: 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":"2025-11-05","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 : 2025-11-04DOI: 10.1016/j.jpaa.2025.108124
Jianbei An
We introduce a way to classify weight subgroups of a block. As an application we classified weight subgroups and proved the Alperin weight conjecture for quasi-isolated 2-blocks of .
{"title":"Weight subgroups of quasi-isolated 2-blocks of the Chevalley groups F4(q)","authors":"Jianbei An","doi":"10.1016/j.jpaa.2025.108124","DOIUrl":"10.1016/j.jpaa.2025.108124","url":null,"abstract":"<div><div>We introduce a way to classify weight subgroups of a block. As an application we classified weight subgroups and proved the Alperin weight conjecture for quasi-isolated 2-blocks of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108124"},"PeriodicalIF":0.8,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475356","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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