Algebras and Representation Theory最新文献_第5页

Symmetry of Derived Delooping Level 派生发展水平的对称性

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-08-01 DOI: 10.1007/s10468-025-10355-4

Ruoyu Guo

引用次数: 0

Notes on Semisimple Monoidal Categories of Rank Two 关于二阶半单一元范畴的注释

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-08-01 DOI: 10.1007/s10468-025-10351-8

Hua Sun, Hui-Xiang Chen, Yinhuo Zhang

引用次数: 0

Gabriel’s Theorem for Infinite Quivers 无限颤抖的加布里埃尔定理

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-29 DOI: 10.1007/s10468-025-10349-2

Nathaniel Gallup, Stephen Sawin

{"title":"Gabriel’s Theorem for Infinite Quivers","authors":"Nathaniel Gallup, Stephen Sawin","doi":"10.1007/s10468-025-10349-2","DOIUrl":"10.1007/s10468-025-10349-2","url":null,"abstract":"<div>We prove a version of Gabriel’s theorem for (possibly infinite dimensional) representations of infinite quivers. More precisely, we show that the representation theory of a quiver (varvec{Omega }) is of unique type (each dimension vector has at most one associated indecomposable) and infinite Krull-Schmidt (every, possibly infinite dimensional, representation is a direct sum of indecomposables) if and only if (varvec{Omega }) is eventually outward and of generalized ADE Dynkin type ((varvec{A_n}), (varvec{D_n}), (varvec{E_6}), (varvec{E_7}), (varvec{E_8}), (varvec{A_infty }), (varvec{A_{infty , infty }}), or (varvec{D_infty })). Furthermore we define an analog of the Euler-Tits form on the space of eventually constant infinite roots and show that a quiver is of generalized ADE Dynkin type if and only if this form is positive definite. In this case the indecomposables are all locally finite-dimensional and eventually constant and correspond bijectively to the positive roots (i.e. those of length (varvec{1})).</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"1015 - 1040"},"PeriodicalIF":0.6,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10349-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Crystals for shifted key polynomials 移位键多项式的晶体

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-28 DOI: 10.1007/s10468-025-10345-6

Eric Marberg, Travis Scrimshaw

{"title":"Crystals for shifted key polynomials","authors":"Eric Marberg, Travis Scrimshaw","doi":"10.1007/s10468-025-10345-6","DOIUrl":"10.1007/s10468-025-10345-6","url":null,"abstract":"<div>This article continues our study of P- and Q-key polynomials, which are (non-symmetric) “partial” Schur P- and Q-functions as well as “shifted” versions of key polynomials. Our main results provide a crystal interpretation of P- and Q-key polynomials, namely, as the characters of certain connected subcrystals of normal crystals associated to the queer Lie superalgebra (mathfrak {q}_n). In the P-key case, the ambient normal crystals are the (mathfrak {q}_n)-crystals studied by Grantcharov et al., while in the Q-key case, these are replaced by the extended (mathfrak {q}_n)-crystals recently introduced by the first author and Tong. Using these constructions, we propose a crystal-theoretic lift of several conjectures about the decomposition of involution Schubert polynomials into P- and Q-key polynomials. We verify these generalized conjectures in a few special cases. Along the way, we establish some miscellaneous results about normal (mathfrak {q}_n)-crystals and Demazure (mathfrak {gl}_n)-crystals.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"921 - 979"},"PeriodicalIF":0.6,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10345-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Automorphism Group of Suzuki’s Hopf Algebra Suzuki Hopf代数的自同构群

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-25 DOI: 10.1007/s10468-025-10346-5

Yuxing Shi, Naihong Hu

引用次数: 0

Gorenstein (mathcal{F}mathcal{P}_n)-Flat Modules and Weak Global Dimensions Gorenstein (mathcal{F}mathcal{P}_n) -平面模和弱全局维

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-24 DOI: 10.1007/s10468-025-10352-7

Víctor Becerril

{"title":"Gorenstein (mathcal{F}mathcal{P}_n)-Flat Modules and Weak Global Dimensions","authors":"Víctor Becerril","doi":"10.1007/s10468-025-10352-7","DOIUrl":"10.1007/s10468-025-10352-7","url":null,"abstract":"<div>In this paper we characterize the relative Gorenstein weak global dimension of the Gorenstein (mathcal {B})-flat R-modules and projectively coresolved Gorenstein (mathcal {B})-flat R-modules recently studied by S. Estrada, A. Iacob, and M. A. Pérez, which are a relativisation of the ones introduced by J. Šaroch and J. Št’ovíchěk. As application we prove that the weak global dimension with respect to the Gorenstein (textrm{FP}_n)-flat R-modules is finite over a Gorenstein n-coherent ring R and in this case coincides with the flat dimension of the right (textrm{FP}_n)-injective R-modules. This result extends the known for Gorenstein flat modules over Iwanaga-Gorenstein and Ding-Chen rings. We also show that there is a close relationship between the relative global dimension of the Gorenstein (textrm{FP}_n)-projectives and the Gorenstein weak global dimension respect to the class of Gorenstein (textrm{FP}_n)-flat R-modules. We also get an hereditary and complete cotorsion triple and consequently a balanced pair.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"1073 - 1091"},"PeriodicalIF":0.6,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10352-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Non-abelian Class Field Theory and Higher Dimensional Noncommutative Tori 非阿贝尔类场论与高维非交换环面

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-18 DOI: 10.1007/s10468-025-10350-9

Igor V. Nikolaev

引用次数: 0

Sequences of ICE-closed Subcategories via Preordered (tau ^{-1})-rigid Modules 通过预购(tau ^{-1}) -刚性模块的ice闭合子类别序列

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-14 DOI: 10.1007/s10468-025-10347-4

Eric J. Hanson

引用次数: 0

Invariants that are Covering Spaces and their Hopf Algebras 覆盖空间的不变量及其Hopf代数

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-07-08 DOI: 10.1007/s10468-025-10343-8

Ehud Meir

{"title":"Invariants that are Covering Spaces and their Hopf Algebras","authors":"Ehud Meir","doi":"10.1007/s10468-025-10343-8","DOIUrl":"10.1007/s10468-025-10343-8","url":null,"abstract":"<div>In a previous paper by the author a universal ring of invariants for algebraic structures of a given type was constructed. This ring is a polynomial algebra that is generated by certain trace diagrams. It was shown that this ring admits the structure of a rational positive self adjoint Hopf algebra (abbreviated rational PSH-algebra), and was conjectured that it always admits a lattice that is a PSH-algebra, a structure that was introduced by Zelevinsky. In this paper we solve this conjecture, showing that the universal ring of invariants splits as the tensor product of rational PSH-algebras that are either polynomial algebras in a single variable, or admit a lattice that is a PSH-algebra. We do so by considering diagrams as topological spaces, and using tools from the theory of covering spaces. As an application we derive a formula that connects Kronecker coefficients with finite index subgroups of free groups and representations of their Weyl groups, and a formula for the number of conjugacy classes of finite index subgroup in a finitely generated group that admits a surjective homomorphism onto the group of integers.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"28 4","pages":"883 - 920"},"PeriodicalIF":0.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-025-10343-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Symmetries of Quiver Schemes 颤振方案的对称性

IF 0.6 4区数学

Algebras and Representation Theory Pub Date : 2025-06-25 DOI: 10.1007/s10468-025-10340-x

Ryo Terada, Daisuke Yamakawa

引用次数: 0