Algebras and Representation Theory最新文献_第3页

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

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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><p>In this paper, we give a more down-to-earth introduction to the connection between Gelfand-Tsetlin modules over <span>(mathfrak {gl}_n)</span> 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 <span>(mathfrak {sl}_n)</span> 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 <span>(>4)</span>, our computers are not adequate to perform these computations.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":null,"pages":null},"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><p>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 <span>(mathcal {O})</span>-operators.</p></div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":null,"pages":null},"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

Two (mathbb {Z})-Graded Infinite Lie Conformal Algebras Related to the Virasoro Conformal Algebra 与维拉索罗共形代数有关的两个 $mathbb {Z}$ -Graded 无限列共形代数

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-02-24 DOI: 10.1007/s10468-024-10260-2

Xiaoqing Yue, Shun Zou

引用次数: 0

Soergel Calculus with Patches 带补丁的索格尔微积分

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-02-23 DOI: 10.1007/s10468-024-10259-9

Leonardo Maltoni

引用次数: 0

Recollements of Derived Categories from Two-Term Big Tilting Complexes 从两期大倾斜复合体衍生类别的重元素

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-02-19 DOI: 10.1007/s10468-024-10258-w

Huabo Xu

引用次数: 0