Journal of Algebra最新文献

{"title":"A 2-dimensional torsion theory on symmetric monoidal categories","authors":"Mariano Messora","doi":"10.1016/j.jalgebra.2025.04.014","DOIUrl":"10.1016/j.jalgebra.2025.04.014","url":null,"abstract":"<div><div>In this paper, we describe a homotopy torsion theory on the category of small symmetric monoidal categories. By using natural isomorphisms as the basis for the nullhomotopy structure, this homotopy torsion theory exhibits some interesting 2-dimensional properties which could be the foundation for a definition of “2-dimensional torsion theory”.</div><div>We choose symmetric 2-groups as torsion objects, thereby generalising a known pointed torsion theory in the category of commutative monoids where abelian groups are taken as torsion objects. In the final part of the paper we carry out an analogous generalisation for the classical torsion theory in the category of abelian groups given by torsion and torsion-free abelian groups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 372-393"},"PeriodicalIF":0.8,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874474","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}

{"title":"Twisted super Yangians of type AIII and their representations","authors":"Kang Lu","doi":"10.1016/j.jalgebra.2025.04.008","DOIUrl":"10.1016/j.jalgebra.2025.04.008","url":null,"abstract":"<div><div>We study the super analogue of the Molev-Ragoucy reflection algebras, which we call twisted super Yangians of type AIII, and classify their finite-dimensional irreducible representations. These superalgebras are coideal subalgebras of the super Yangian <span><math><mi>Y</mi><mo>(</mo><msub><mrow><mi>gl</mi></mrow><mrow><mi>m</mi><mo>|</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span> and are associated with symmetric pairs of type AIII in Cartan's classification. We establish the Schur-Weyl type duality between degenerate affine Hecke algebras of type BC and twisted super Yangians.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 74-132"},"PeriodicalIF":0.8,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869707","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}

{"title":"Gröbner basis and Krull dimension of the Lovász-Saks-Sherijver ideal associated to a tree","authors":"Mohammad Farrokhi D. G. ,&nbsp;Ali Akbar Yazdan Pour","doi":"10.1016/j.jalgebra.2025.03.049","DOIUrl":"10.1016/j.jalgebra.2025.03.049","url":null,"abstract":"<div><div>Let <span><math><mi>K</mi></math></span> be a field and <em>n</em> be a positive integer. Let <span><math><mi>Γ</mi><mo>=</mo><mo>(</mo><mo>[</mo><mi>n</mi><mo>]</mo><mo>,</mo><mi>E</mi><mo>)</mo></math></span> be a simple graph, where <span><math><mo>[</mo><mi>n</mi><mo>]</mo><mo>=</mo><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></math></span>. If <span><math><mi>S</mi><mo>=</mo><mi>K</mi><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></math></span> is a polynomial ring, then the graded ideal<span><span><span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mi>K</mi></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo><mo>=</mo><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>+</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>y</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>:</mo><mspace></mspace><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo><mo>∈</mo><mi>E</mi><mo>(</mo><mi>Γ</mi><mo>)</mo><mo>)</mo></mrow><mo>⊂</mo><mi>S</mi><mo>,</mo></math></span></span></span> is called the Lovász-Saks-Schrijver ideal, LSS-ideal for short, of Γ with respect to <span><math><mi>K</mi></math></span>. In the present paper, we compute a Gröbner basis of this ideal with respect to lexicographic ordering induced by <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&gt;</mo><mo>⋯</mo><mo>&gt;</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>&gt;</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&gt;</mo><mo>⋯</mo><mo>&gt;</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> when <span><math><mi>Γ</mi><mo>=</mo><mi>T</mi></math></span> is a tree. As a result, we show that it is independent of the choice of the ground field <span><math><mi>K</mi></math></span> and compute the Hilbert series of <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>T</mi></mrow><mrow><mi>K</mi></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo></math></span>. Finally, we present concrete combinatorial formulas to obtain the Krull dimension of <span><math><mi>S</mi><mo>/</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>T</mi></mrow><mrow><mi>K</mi></mrow></msubsup><mo>(</mo><mn>2</mn><mo>)</mo></math></span> as well as lower and upper bounds for Krull dimension.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 224-252"},"PeriodicalIF":0.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869714","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}

{"title":"A∞-deformations of zigzag algebras via Ginzburg dg algebras","authors":"Junyang Liu ,&nbsp;Zhengfang Wang","doi":"10.1016/j.jalgebra.2025.03.057","DOIUrl":"10.1016/j.jalgebra.2025.03.057","url":null,"abstract":"<div><div>This note aims to give a short proof of the recent result due to Etgü–Lekili (2017) and Lekili–Ueda (2021): the zigzag algebra of any finite tree over a field of characteristic 0 is intrinsically formal if and only if the tree is of type <em>ADE</em>. We also complete the proof of this result by considering a field of arbitrary characteristic for type <em>E</em>, which was still open.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 360-371"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868918","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}

{"title":"The minimal model program for arithmetic surfaces enriched by a Brauer class","authors":"Daniel Chan ,&nbsp;Colin Ingalls","doi":"10.1016/j.jalgebra.2025.03.047","DOIUrl":"10.1016/j.jalgebra.2025.03.047","url":null,"abstract":"<div><div>We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class <em>β</em>. When <em>β</em> has prime index <span><math><mi>p</mi><mo>&gt;</mo><mn>5</mn></math></span>, we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify <em>β</em>-terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 475-511"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864109","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}

{"title":"On the root system of a Kac-Moody superalgebra","authors":"Maria Gorelik,&nbsp;Shay Kinamon Kerbis","doi":"10.1016/j.jalgebra.2025.03.055","DOIUrl":"10.1016/j.jalgebra.2025.03.055","url":null,"abstract":"<div><div>In this paper we extend several results about root systems of Kac-Moody algebras to superalgebra context. In particular, we describe the root bases and the sets of imaginary roots.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"678 ","pages":"Pages 133-195"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869708","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}

{"title":"Categories of hypermagmas, hypergroups, and related hyperstructures","authors":"So Nakamura,&nbsp;Manuel L. Reyes","doi":"10.1016/j.jalgebra.2025.03.056","DOIUrl":"10.1016/j.jalgebra.2025.03.056","url":null,"abstract":"<div><div>In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains categories with desirable features such as completeness and cocompleteness, free functors, regularity, and closed monoidal structures. We show by counterexamples that such constructions cannot be carried out within the category of canonical hypergroups. This suggests that (commutative) unital, reversible hypermagmas—which we call <em>mosaics</em>—form a worthwhile generalization of (canonical) hypergroups from the categorical perspective. Notably, mosaics contain pointed simple matroids as a subcategory, and projective geometries as a full subcategory.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 408-474"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859698","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}

{"title":"Schubert determinantal ideals are Hilbertian","authors":"Ada Stelzer,&nbsp;Alexander Yong","doi":"10.1016/j.jalgebra.2025.04.005","DOIUrl":"10.1016/j.jalgebra.2025.04.005","url":null,"abstract":"<div><div>Abhyankar defined an ideal to be <em>Hilbertian</em> if its Hilbert polynomial coincides with its Hilbert function for all nonnegative integers. In 1984, he proved that the ideal of <span><math><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-order minors of a generic <span><math><mi>p</mi><mo>×</mo><mi>q</mi></math></span> matrix is Hilbertian. We give a different proof and a generalization to the <em>Schubert determinantal ideals</em> introduced by Fulton in 1992. Our proof reduces to a simple upper bound for the Castelnuovo–Mumford regularity of these ideals. We further indicate the pervasiveness of the Hilbertian property in Schubert geometry.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 278-293"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143864477","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}

{"title":"Finite groups with exactly two nonlinear irreducible p-Brauer characters","authors":"Fuming Jiang ,&nbsp;Yu Zeng","doi":"10.1016/j.jalgebra.2025.04.006","DOIUrl":"10.1016/j.jalgebra.2025.04.006","url":null,"abstract":"<div><div>Let <em>p</em> be a prime. We classify the finite groups having exactly two irreducible <em>p</em>-Brauer characters of degree larger than one. The case, where the finite groups have orders not divisible by <em>p</em>, was done by P. Pálfy in 1981.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"677 ","pages":"Pages 294-326"},"PeriodicalIF":0.8,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868910","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}

{"title":"Twisted unipotent groups","authors":"Ken A. Brown ,&nbsp;Shlomo Gelaki","doi":"10.1016/j.jalgebra.2025.03.043","DOIUrl":"10.1016/j.jalgebra.2025.03.043","url":null,"abstract":"<div><div>We study the algebraic structure and representation theory of the Hopf algebras <span><math><mmultiscripts><mrow><mi>O</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi></mrow><none></none></mmultiscripts><msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>J</mi></mrow></msub></math></span> when <em>G</em> is an affine algebraic unipotent group over <span><math><mi>C</mi></math></span> with <span><math><mrow><mi>dim</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>n</mi></math></span> and <em>J</em> is a Hopf 2-cocycle for <em>G</em>. The cotriangular Hopf algebras <span><math><mmultiscripts><mrow><mi>O</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi></mrow><none></none></mmultiscripts><msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>J</mi></mrow></msub></math></span> have the same coalgebra structure as <span><math><mi>O</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> but a deformed multiplication. We show that they are involutive <em>n</em>-step iterated Hopf Ore extensions of derivation type. The 2-cocycle <em>J</em> has as support a closed subgroup <em>T</em> of <em>G</em>, and <span><math><mmultiscripts><mrow><mi>O</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi></mrow><none></none></mmultiscripts><msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>J</mi></mrow></msub></math></span> is a crossed product <span><math><mi>S</mi><msub><mrow><mi>#</mi></mrow><mrow><mi>σ</mi></mrow></msub><mi>U</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, where <span><math><mi>t</mi></math></span> is the Lie algebra of <em>T</em> and <em>S</em> is a deformed coideal subalgebra. Each simple <span><math><mmultiscripts><mrow><mi>O</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi></mrow><none></none></mmultiscripts><msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>J</mi></mrow></msub></math></span>-module factors through a unique quotient algebra <span><math><mmultiscripts><mrow><mi>O</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi></mrow><none></none></mmultiscripts><msub><mrow><mo>(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>J</mi></mrow></msub></math></span>. These quotient algebras are parametrised by the double cosets <em>TgT</em> of <em>T</em> in <em>G</em>, and form an obvious direction for further study. The finite dimensional simple <span><math><mmultiscripts><mrow><mi>O</mi></mrow><mprescripts></mprescripts><mrow><mi>J</mi></mrow><none></none></mmultiscripts><msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mi>J</mi></mrow></msub></math></span>-modules are all 1-dimensional, so form a group Γ, which we prove to be an explicitly determined closed subgroup of <em>G</em>. A selection of examples illustrate our results.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"676 ","pages":"Pages 318-377"},"PeriodicalIF":0.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143855779","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}