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On representations of permutation groups and their orbit categories 论置换群的表示及其轨道范畴
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-04-01 Epub Date: 2026-03-26 DOI: 10.1016/j.jpaa.2026.108241
Liping Li
{"title":"On representations of permutation groups and their orbit categories","authors":"Liping Li","doi":"10.1016/j.jpaa.2026.108241","DOIUrl":"10.1016/j.jpaa.2026.108241","url":null,"abstract":"<div><div>Given an infinite set Ω and a ring <em>R</em> as well as a group <em>G</em> acting on them, we show that <em>G</em> and a subgroup <em>H</em> share the same canonical relational structure on Ω if and only if the restriction functor gives an equivalence from the category of discrete representations of <em>G</em> to that of <em>H</em>. Moreover, the age of this relational structure satisfies the strong amalgamation property if and only if there is a canonical isomorphism from the category of finite substructures of Ω and embeddings to the opposite category of the orbit category of <em>G</em>. As an application, we prove that finitely generated discrete representations of highly homogeneous groups over the polynomial ring <span><math><mi>k</mi><mo>[</mo><mi>Ω</mi><mo>]</mo></math></span> are Noetherian.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 4","pages":"Article 108241"},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147602050","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}
引用次数: 0
Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property 不符合弱Lefschetz性质的过山车式Gorenstein代数和Koszul代数
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-04-01 Epub Date: 2026-03-26 DOI: 10.1016/j.jpaa.2026.108238
Thiago Holleben , Lisa Nicklasson
{"title":"Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property","authors":"Thiago Holleben ,&nbsp;Lisa Nicklasson","doi":"10.1016/j.jpaa.2026.108238","DOIUrl":"10.1016/j.jpaa.2026.108238","url":null,"abstract":"<div><div>Inspired by the Roller Coaster Theorem from graph theory, we prove the existence of Artinian Gorenstein algebras with unconstrained Hilbert series, which we call <em>Roller Coaster algebras</em>. Our construction relies on Nagata idealization of quadratic monomial algebras defined by whiskered graphs. The monomial algebras are interesting in their own right, as our results suggest that Artinian level algebras defined by quadratic monomial ideals rarely have the weak Lefschetz property. In addition, we discover a large family of G-quadratic Gorenstein algebras failing the weak Lefschetz property.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 4","pages":"Article 108238"},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147602048","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}
引用次数: 0
Transposing cartesian and other structure in double categories 调换双范畴中的笛卡儿结构和其他结构
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-04-01 Epub Date: 2026-03-30 DOI: 10.1016/j.jpaa.2026.108233
Evan Patterson
{"title":"Transposing cartesian and other structure in double categories","authors":"Evan Patterson","doi":"10.1016/j.jpaa.2026.108233","DOIUrl":"10.1016/j.jpaa.2026.108233","url":null,"abstract":"<div><div>The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program of cartesian bicategories, the precise relationship between the double-categorical and bicategorical approaches has so far remained mysterious, except in special cases. We provide a formal connection by showing that every double category with iso-strong finite products, and in particular every cartesian equipment, has an underlying cartesian bicategory. To do so, we develop broadly applicable techniques for transposing natural transformations and adjunctions between double categories, extending a line of previous work rooted in the concepts of companions and conjoints.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 4","pages":"Article 108233"},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147602046","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}
引用次数: 0
On monoids up to symmetry 在单群上直到对称
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-04-01 Epub Date: 2026-03-27 DOI: 10.1016/j.jpaa.2026.108243
Dinh Van Le , Tim Römer , Nguyen Thi Vien
{"title":"On monoids up to symmetry","authors":"Dinh Van Le ,&nbsp;Tim Römer ,&nbsp;Nguyen Thi Vien","doi":"10.1016/j.jpaa.2026.108243","DOIUrl":"10.1016/j.jpaa.2026.108243","url":null,"abstract":"<div><div>We study monoids in <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></msup></math></span> that are invariant under the action of the infinite symmetric group Sym. Our main result establishes a local–global principle characterizing equivariant finite generation for arbitrary Sym-invariant monoids, extending earlier results that required additional assumptions. We further analyze local–global phenomena for other fundamental properties, including positivity, normality, seminormality, and simplicity. In addition, we obtain structural results for symmetric monoids, including characterizations of positivity and non-positivity, a description of their groups of units, and explicit formulas for the ranks of local symmetric monoids and stabilizing Sym-invariant chains.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 4","pages":"Article 108243"},"PeriodicalIF":0.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147602072","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}
引用次数: 0
Measuring comodules and enrichment 测量模块和富集
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-03-01 Epub Date: 2026-02-24 DOI: 10.1016/j.jpaa.2026.108211
Martin Hyland , Ignacio López Franco , Christina Vasilakopoulou
{"title":"Measuring comodules and enrichment","authors":"Martin Hyland ,&nbsp;Ignacio López Franco ,&nbsp;Christina Vasilakopoulou","doi":"10.1016/j.jpaa.2026.108211","DOIUrl":"10.1016/j.jpaa.2026.108211","url":null,"abstract":"<div><div>This paper extends the theory of universal measuring comonoids to modules and comodules in braided monoidal categories. We generalise the universal measuring comodule <span><math><mi>Q</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, originally introduced for modules over <span><math><mi>k</mi></math></span>-algebras when <span><math><mi>k</mi></math></span> is a field, to arbitrary braided monoidal categories. In order to establish its existence, we prove a representability theorem for presheaves on opfibred categories and an adjoint functor theorem for opfibred functors. The global categories of modules and comodules, fibred and opfibred over monoids and comonoids respectively, are shown to exhibit an enrichment of modules in comodules. Additionally, we use our framework to study higher derivations of algebras and modules, defining along the way the non-commutative Hasse-Schmidt algebra.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108211"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422568","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}
引用次数: 0
Morita invariants of quasitriangular coideal subalgebras 拟三角共理想子代数的Morita不变量
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108210
Monique Müller , Chelsea Walton
{"title":"Morita invariants of quasitriangular coideal subalgebras","authors":"Monique Müller ,&nbsp;Chelsea Walton","doi":"10.1016/j.jpaa.2026.108210","DOIUrl":"10.1016/j.jpaa.2026.108210","url":null,"abstract":"<div><div>We use representations of braid groups of Coxeter types BC and D to produce invariants of representation categories of quasitriangular coideal subalgebras. Such categories form a prevalent class of braided module categories. This is analogous to how representations of braid groups of Coxeter type A produce invariants of representation categories of quasitriangular Hopf algebras, a prevalent class of braided monoidal categories. This work also includes concrete examples, and classification results for <em>K</em>-matrices of quasitriangular coideal subalgebras.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108210"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422569","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}
引用次数: 0
On Rota-Baxter vertex operator algebras 关于Rota-Baxter顶点算子代数
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108202
Chengming Bai , Li Guo , Jianqi Liu , Xiaoyan Wang
{"title":"On Rota-Baxter vertex operator algebras","authors":"Chengming Bai ,&nbsp;Li Guo ,&nbsp;Jianqi Liu ,&nbsp;Xiaoyan Wang","doi":"10.1016/j.jpaa.2026.108202","DOIUrl":"10.1016/j.jpaa.2026.108202","url":null,"abstract":"<div><div>Rota-Baxter operators, which can be viewed as the integral counterpart of derivations on algebras and operator forms of the classical Yang-Baxter equation, are defined and studied for vertex (operator) algebras. Examples of such operators are constructed for various vertex operator algebras. The closely related notion of dendriform algebras is also defined for vertex operator algebras. It is shown that the Rota-Baxter operators and dendriform structures give rise to new examples of vertex (Leibniz) algebras and vertex algebras without vacuum. The classical relations among dendriform algebras, associative algebras, Rota-Baxter algebras, and pre-Lie algebras are also extended to their vertex algebra analogs.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108202"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422571","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}
引用次数: 0
Two invariant subalgebras of rational Cherednik algebras 有理Cherednik代数的两个不变子代数
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-03-01 Epub Date: 2026-02-05 DOI: 10.1016/j.jpaa.2026.108190
Gwyn Bellamy, Misha Feigin, Niall Hird
{"title":"Two invariant subalgebras of rational Cherednik algebras","authors":"Gwyn Bellamy,&nbsp;Misha Feigin,&nbsp;Niall Hird","doi":"10.1016/j.jpaa.2026.108190","DOIUrl":"10.1016/j.jpaa.2026.108190","url":null,"abstract":"<div><div>Originally motivated by connections to integrable systems, two natural subalgebras of the rational Cherednik algebra have been considered in the literature. The first is the subalgebra of all degree zero elements and the second is the Dunkl angular momentum subalgebra.</div><div>In this article, we study the ring-theoretic and homological properties of these algebras. Our approach is to realise them as rings of invariants under the action of certain reductive subgroups of <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. This allows us to describe their centres. Moreover, we show that they are Auslander–Gorenstein and Cohen–Macaulay and, at <span><math><mi>t</mi><mo>=</mo><mn>0</mn></math></span>, give rise to prime PI-algebras whose PI-degree we compute.</div><div>Since the degree zero subalgebra can be realized as the ring of invariants for the maximal torus <span><math><mi>T</mi><mo>⊂</mo><msub><mrow><mi>SL</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and the action of this torus on the rational Cherednik algebra is Hamiltonian, we also consider its (quantum) Hamiltonian reduction with respect to T. At <span><math><mi>t</mi><mo>=</mo><mn>1</mn></math></span>, the quantum Hamiltonian reduction of the spherical subalgebra is a filtered quantization of the quotient of the minimal nilpotent orbit closure <span><math><msub><mrow><mover><mrow><mi>O</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>min</mi></mrow></msub></math></span> in <span><math><mrow><mi>gl</mi></mrow><mo>(</mo><mi>n</mi><mo>)</mo></math></span> by the reflection group <em>W</em>. At <span><math><mi>t</mi><mo>=</mo><mn>0</mn></math></span>, we get a graded Poisson deformation of the symplectic singularity <span><math><msub><mrow><mover><mrow><mi>O</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>min</mi></mrow></msub><mo>/</mo><mi>W</mi></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108190"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146175450","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}
引用次数: 0
Skew Symmetric Extended Affine Lie algebras 斜对称扩展仿射李代数
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-03-01 Epub Date: 2026-02-05 DOI: 10.1016/j.jpaa.2026.108188
S. Eswara Rao , Priyanshu Chakraborty
{"title":"Skew Symmetric Extended Affine Lie algebras","authors":"S. Eswara Rao ,&nbsp;Priyanshu Chakraborty","doi":"10.1016/j.jpaa.2026.108188","DOIUrl":"10.1016/j.jpaa.2026.108188","url":null,"abstract":"<div><div>For any skew symmetric matrix over complex numbers, we introduce an EALA and it is called Skew Symmetric Extended Affine Lie Algebra (SSEALA). This way we get a large class of EALAs and most often they are non-isomorphic. In this paper we study irreducible integrable modules for SSEALA with finite dimensional weight spaces. We classify all such modules in the level zero case with non degenerate skew symmetric matrix.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108188"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146154334","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}
引用次数: 0
Infinitesimal R-matrices for some families of Hopf algebras 一些Hopf代数族的无穷小r矩阵
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2026-03-01 Epub Date: 2026-02-23 DOI: 10.1016/j.jpaa.2026.108205
Lucrezia Bottegoni , Fabio Renda , Andrea Sciandra
{"title":"Infinitesimal R-matrices for some families of Hopf algebras","authors":"Lucrezia Bottegoni ,&nbsp;Fabio Renda ,&nbsp;Andrea Sciandra","doi":"10.1016/j.jpaa.2026.108205","DOIUrl":"10.1016/j.jpaa.2026.108205","url":null,"abstract":"<div><div>Given a bialgebra <em>H</em> such that the associated trivial topological bialgebra <span><math><mi>H</mi><mo>[</mo><mo>[</mo><mi>ħ</mi><mo>]</mo><mo>]</mo></math></span> admits a quasitriangular structure <span><math><mover><mrow><mi>R</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>=</mo><mi>R</mi><mo>(</mo><mn>1</mn><mo>⊗</mo><mn>1</mn><mo>+</mo><mi>ħ</mi><mi>χ</mi><mo>+</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>ħ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>)</mo></math></span>, one gets a distinguished element <span><math><mi>χ</mi><mo>∈</mo><mi>H</mi><mo>⊗</mo><mi>H</mi></math></span> which is an infinitesimal <span><math><mi>R</mi></math></span>-matrix, according to the definition given in <span><span>[1]</span></span>. In this paper we classify infinitesimal <span><math><mi>R</mi></math></span>-matrices for some families of well-known Hopf algebras, among which are the generalized Kac–Paljutkin Hopf algebras <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></msub></math></span>, the Radford Hopf algebras <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></msub></math></span>, and the Hopf algebras <span><math><mi>E</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"230 3","pages":"Article 108205"},"PeriodicalIF":0.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147422585","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}
引用次数: 0
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