Algebras and Representation Theory最新文献_第4页

Twisted Representations of the Extended Heisenberg-Virasoro Vertex Operator Algebra 扩展海森堡-维拉索罗顶点算子代数的扭曲表示

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-30 DOI: 10.1007/s10468-024-10270-0

Hongyan Guo, Huaimin Li

{"title":"Twisted Representations of the Extended Heisenberg-Virasoro Vertex Operator Algebra","authors":"Hongyan Guo, Huaimin Li","doi":"10.1007/s10468-024-10270-0","DOIUrl":"10.1007/s10468-024-10270-0","url":null,"abstract":"<div>In this paper, we study simple weak and ordinary twisted modules of the extended Heisenberg-Virasoro vertex operator algebra (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)). We first determine the full automorphism groups of (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)) for all (ell _{1}, ell _{2},ell _{3},Fin {mathbb C}). They are isomorphic to certain subgroups of the general linear group (text {GL}_{2}({mathbb C})). Then for a family of finite order automorphisms (sigma _{r_{1},r_{2}}) of (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)), we show that weak (sigma _{r_{1},r_{2}})-twisted (V_{tilde{mathcal {L}}_{F}}(ell _{123},0))-modules are in one-to-one correspondence with restricted modules of certain Lie algebras of level (ell _{123}), where (r_{1}, r_2in {mathbb N}). By this identification and vertex algebra theory, we give complete lists of simple ordinary (sigma _{r_{1},r_{2}})-twisted modules over (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)). The results depend on whether F or (ell _{2}) is zero or not. Furthermore, simple weak (sigma _{r_{1},r_{2}})-twisted (V_{tilde{mathcal {L}}_{F}}(ell _{123},0))-modules are also investigated. For this, we introduce and study restricted modules (including Whittaker modules) of a new Lie algebra (mathcal {L}_{r_{1},r_{2}}) which is related to the mirror Heisenberg-Virasoro algebra.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1563 - 1580"},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

The Mukai Conjecture for Fano Quiver Moduli 法诺震颤模的向猜想

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-26 DOI: 10.1007/s10468-024-10268-8

Markus Reineke

引用次数: 0

Galleries for Root Subsystems 根子系统图库

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-24 DOI: 10.1007/s10468-024-10269-7

Vladimir Shchigolev

引用次数: 0

Decompositions of Infinite-Dimensional (A_{infty , infty }) Quiver Representations 无穷维 $$A_{infty , infty }$$ 箙代表的分解

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-19 DOI: 10.1007/s10468-024-10267-9

Nathaniel Gallup, Stephen Sawin

{"title":"Decompositions of Infinite-Dimensional (A_{infty , infty }) Quiver Representations","authors":"Nathaniel Gallup, Stephen Sawin","doi":"10.1007/s10468-024-10267-9","DOIUrl":"10.1007/s10468-024-10267-9","url":null,"abstract":"<div>Gabriel’s Theorem states that the quivers which have finitely many isomorphism classes of indecomposable representations are exactly those with underlying graph one of the ADE Dynkin diagrams and that the indecomposables are in bijection with the positive roots of this graph. When the underlying graph is (varvec{A_n}), these indecomposable representations are thin (either 0 or 1 dimensional at every vertex) and in bijection with the connected subquivers. Using linear algebraic methods we show that every (possibly infinite-dimensional) representation of a quiver with underlying graph (varvec{A_{infty , infty }}) is infinite Krull-Schmidt, i.e. a direct sum of indecomposables, as long as the arrows in the quiver eventually point outward. We furthermore prove that these indecomposable are again thin and in bijection with both the connected subquivers and the limits of the positive roots of (varvec{A_{infty , infty }}) with respect to a certain uniform topology on the root space. Finally we give an example of an (varvec{A_{infty , infty }}) quiver which is not infinite Krull-Schmidt and hence necessarily is not eventually-outward.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1513 - 1535"},"PeriodicalIF":0.5,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10267-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626695","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

Recasting the Hazrat Conjecture: Relating Shift Equivalence to Graded Morita Equivalence 重塑哈兹拉特猜想：移位等价性与梯度莫里塔等价性的关系

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-09 DOI: 10.1007/s10468-024-10266-w

Gene Abrams, Efren Ruiz, Mark Tomforde

引用次数: 0

Gelfand-Tsetlin Modules: Canonicity and Calculations 格尔凡-采特林模块：可达性和计算

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-03-27 DOI: 10.1007/s10468-024-10264-y

Turner Silverthorne, Ben Webster

{"title":"Gelfand-Tsetlin Modules: Canonicity and Calculations","authors":"Turner Silverthorne, Ben Webster","doi":"10.1007/s10468-024-10264-y","DOIUrl":"10.1007/s10468-024-10264-y","url":null,"abstract":"<div>In this paper, we give a more down-to-earth introduction to the connection between Gelfand-Tsetlin modules over (mathfrak {gl}_n) and diagrammatic KLRW algebras and develop some of its consequences. In addition to a new proof of this description of the category Gelfand-Tsetlin modules appearing in earlier work, we show three new results of independent interest: (1) we show that every simple Gelfand-Tsetlin module is a canonical module in the sense of Early, Mazorchuk and Vishnyakova, and characterize when two maximal ideals have isomorphic canonical modules, (2) we show that the dimensions of Gelfand-Tsetlin weight spaces in simple modules can be computed using an appropriate modification of Leclerc’s algorithm for computing dual canonical bases, and (3) we construct a basis of the Verma modules of (mathfrak {sl}_n) which consists of generalized eigenvectors for the Gelfand-Tsetlin subalgebra. Furthermore, we present computations of multiplicities and Gelfand-Kirillov dimensions for all integral Gelfand-Tsetlin modules in ranks 3 and 4; unfortunately, for ranks (>4), our computers are not adequate to perform these computations.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1405 - 1455"},"PeriodicalIF":0.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Restricted Injective Dimensions over Cohen-Macaulay Rings 科恩-麦考莱环上的限制注入维数

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-03-19 DOI: 10.1007/s10468-024-10262-0

Michal Hrbek, Giovanna Le Gros

引用次数: 0

Commutativity Preservers of Incidence Algebras 发生代数的交换性保全器

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-03-19 DOI: 10.1007/s10468-024-10265-x

Érica Z. Fornaroli, Mykola Khrypchenko, Ednei A. Santulo Jr

引用次数: 0

Criterion for Quasi-Heredity 准危险性标准

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-03-12 DOI: 10.1007/s10468-024-10263-z

Yuichiro Goto

引用次数: 0

Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras 罗塔-巴克斯特列双桥、经典杨-巴克斯特方程和特殊 L-树枝状双桥

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-02-28 DOI: 10.1007/s10468-024-10261-1

Chengming Bai, Li Guo, Guilai Liu, Tianshui Ma

{"title":"Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras","authors":"Chengming Bai, Li Guo, Guilai Liu, Tianshui Ma","doi":"10.1007/s10468-024-10261-1","DOIUrl":"10.1007/s10468-024-10261-1","url":null,"abstract":"<div>This paper extends the well-known fact that a Rota-Baxter operator of weight 0 on a Lie algebra induces a pre-Lie algebra, to the level of bialgebras. We first show that a nondegenerate symmetric bilinear form that is invariant on a Rota-Baxter Lie algebra of weight 0 gives such a form that is left-invariant on the induced pre-Lie algebra and thereby gives a special L-dendriform algebra. This fact is obtained as a special case of Rota-Baxter Lie algebras with an adjoint-admissible condition, for a representation of the Lie algebra to admit a representation of the Rota-Baxter Lie algebra on the dual space. This condition can also be naturally formulated for Manin triples of Rota-Baxter Lie algebras, which can in turn be characterized in terms of bialgebras, thereby extending the Manin triple approach to Lie bialgebras. In the case of weight 0, the resulting Rota-Baxter Lie bialgebras give rise to special L-dendriform bialgebras, lifting the aforementioned connection that a Rota-Baxter Lie algebra induces a pre-Lie algebra to the level of bialgebras. The relationship between these two classes of bialgebras is also studied in terms of the coboundary cases, classical Yang-Baxter equations and (mathcal {O})-operators.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1347 - 1372"},"PeriodicalIF":0.5,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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