Journal of Algebra最新文献_第10页

Full conformal oscillator representations of odd orthogonal Lie algebras and combinatorial identities 奇正交李代数的全共形振子表示与组合恒等式

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.04.048

Zhenyu Zhou , Xiaoping Xu

{"title":"Full conformal oscillator representations of odd orthogonal Lie algebras and combinatorial identities","authors":"Zhenyu Zhou , Xiaoping Xu","doi":"10.1016/j.jalgebra.2025.04.048","DOIUrl":"10.1016/j.jalgebra.2025.04.048","url":null,"abstract":"<div><div>Zhao and the second author (2013) constructed a functor from <math><mi>o</mi><mo>(</mo><mi>k</mi><mo>)</mo></math>-Mod to <math><mi>o</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo></math>-Mod. In this paper, we use the functor successively to obtain an inhomogeneous first-order differential operator realization for any highest-weight representation of <math><mi>o</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></math> in <math><msup><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math> variables. When the highest weight is dominant integral, we find a span set for the corresponding finite-dimensional irreducible module. One can use the result to study tensor decomposition of finite-dimensional irreducible modules by solving certain first-order linear partial differential equations, and thereby obtain the corresponding physically interested Clebsch-Gordan coefficients and exact solutions of Knizhnik-Zamolodchikov equation in WZW model of conformal field theory. We also find an equation of counting the dimension of an irreducible <math><mi>o</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></math>-module in terms of certain alternating sum of the dimensions of irreducible <math><mi>o</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math>-modules. In the case of the Steinberg modules, we obtain new combinatorial identities of classical type.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"681 ","pages":"Pages 62-106"},"PeriodicalIF":0.8,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170365","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

Poisson pseudoalgebras 泊松pseudoalgebras

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.04.044

Bojko Bakalov , Ju Wang

{"title":"Poisson pseudoalgebras","authors":"Bojko Bakalov , Ju Wang","doi":"10.1016/j.jalgebra.2025.04.044","DOIUrl":"10.1016/j.jalgebra.2025.04.044","url":null,"abstract":"<div><div>For any cocommutative Hopf algebra H and a left H-module V, we construct an operad <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>H</mi></mrow><mrow><mi>c</mi><mi>l</mi></mrow></msubsup><mo>(</mo><mi>V</mi><mo>)</mo></math>, which in the special case when H is the algebra of polynomials in one variable reduces to the classical operad <math><msup><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>l</mi></mrow></msup><mo>(</mo><mi>V</mi><mo>)</mo></math> of [5]. Morphisms from the Lie operad to <math><msup><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>l</mi></mrow></msup><mo>(</mo><mi>V</mi><mo>)</mo></math> correspond to Poisson vertex algebra structures on V. Likewise, our operad <math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>H</mi></mrow><mrow><mi>c</mi><mi>l</mi></mrow></msubsup><mo>(</mo><mi>V</mi><mo>)</mo></math> gives rise to the notion of a Poisson pseudoalgebra; thus extending the notion of a Lie pseudoalgebra from [1]. As a byproduct of our construction, we introduce two cohomology theories for Poisson pseudoalgebras, generalizing the variational and classical cohomology of Poisson vertex algebras.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"679 ","pages":"Pages 117-168"},"PeriodicalIF":0.8,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166622","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

Chevalley bases for elliptic extended affine Lie algebras of type A1 A1型椭圆扩展仿射李代数的Chevalley基

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.04.043

S. Azam

引用次数: 0

The stable module category and model structures for hierarchically defined groups 为分层定义的组提供稳定的模块类别和模型结构

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.05.008

Gregory Kendall

引用次数: 0

A characterization of varieties of algebras of proper central exponent greater than two 中心指数大于2的各种代数的性质

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.05.005

Francesca S. Benanti , Angela Valenti

{"title":"A characterization of varieties of algebras of proper central exponent greater than two","authors":"Francesca S. Benanti , Angela Valenti","doi":"10.1016/j.jalgebra.2025.05.005","DOIUrl":"10.1016/j.jalgebra.2025.05.005","url":null,"abstract":"<div><div>Let F be a field of characteristic zero and let <math><mi>V</mi></math> be a variety of associative F-algebras. In [19] Regev introduced a numerical sequence measuring the growth of the proper central polynomials of a generating algebra of <math><mi>V</mi></math>. Such sequence <math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>(</mo><mi>V</mi><mo>)</mo><mo>,</mo><mspace></mspace><mi>n</mi><mo>≥</mo><mn>1</mn></math>, is called the sequence of proper central polynomials of <math><mi>V</mi></math> and in [12], [13] the authors computed its exponential growth. This is an invariant of the variety. They also showed that <math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>(</mo><mi>V</mi><mo>)</mo></math> either grows exponentially or is polynomially bounded.</div><div>The purpose of this paper is to characterize the varieties of associative algebras whose exponential growth of <math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>(</mo><mi>V</mi><mo>)</mo></math> is greater than two. As a consequence, we find a characterization of the varieties whose corresponding exponential growth is equal to two.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"679 ","pages":"Pages 96-116"},"PeriodicalIF":0.8,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166642","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

Linear characters for blocks with cyclic defect 具有循环缺陷的块的线性特性

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.04.046

Alexandre Turull

{"title":"Linear characters for blocks with cyclic defect","authors":"Alexandre Turull","doi":"10.1016/j.jalgebra.2025.04.046","DOIUrl":"10.1016/j.jalgebra.2025.04.046","url":null,"abstract":"<div><div>We show that associated with each p-block B with non trivial cyclic defect group D of a finite group are two linear characters <math><msub><mrow><mi>α</mi></mrow><mrow><mi>B</mi></mrow></msub></math> and <math><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></math> of a cyclic group E of order e. Here e is the number of non exceptional irreducible characters that B has. The first character <math><msub><mrow><mi>α</mi></mrow><mrow><mi>B</mi></mrow></msub></math> describes the action of E on D. The second character <math><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></math> arises from certain field extensions. The order of <math><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></math> is the p-local Schur index of any exceptional <math><mi>χ</mi><mo>∈</mo><mi>Irr</mi><mo>(</mo><mi>B</mi><mo>)</mo></math>, giving an alternative description of this invariant to the one given by Benard [1]. From the relationship of <math><msub><mrow><mi>α</mi></mrow><mrow><mi>B</mi></mrow></msub></math> and <math><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></math> we give an alternative description to the one given by Nebe [6] of the invariant associated with each exceptional <math><mi>χ</mi><mo>∈</mo><mi>Irr</mi><mo>(</mo><mi>B</mi><mo>)</mo></math>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"681 ","pages":"Pages 22-45"},"PeriodicalIF":0.8,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169746","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

Semiorthogonal decompositions for generalised Severi-Brauer schemes 广义Severi-Brauer格式的半正交分解

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.04.038

Ajneet Dhillon, Sayantan Roy-Chowdhury

引用次数: 0

A reformulation of the conjecture of Prasad and Takloo-Bighash 对Prasad和taklo - bighash猜想的重新表述

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-05-26 DOI: 10.1016/j.jalgebra.2025.05.007

Miyu Suzuki

引用次数: 0

Generalised power series determined by linear recurrence relations 由线性递归关系确定的广义幂级数