Computation of the Homology of the Complexes of Finite Verma Modules for ${K}_{4}^{\prime }$

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2022-12-21 DOI:10.1007/s10468-022-10176-9

Lucia Bagnoli

引用次数: 0

Abstract

We compute the homology of the complexes of finite Verma modules over the annihilation superalgebra $\mathcal {A}({K}_{4}^{\prime })$, associated with the conformal superalgebra ${K}_{4}^{\prime }$, obtained in Bagnoli and Caselli (J. Math. Phys. 63, 091701, 2022). We use the computation of the homology in order to provide an explicit realization of all the irreducible quotients of finite Verma modules over $\mathcal {A}({K}_{4}^{\prime })$.

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${K}_{4}^{\素数}$有限Verma模复合体的同调计算

我们计算了湮没超代数$\mathcal {A}({K}_{4}^{\prime })上有限韦尔马模块复数的同调，它与共形超代数\({K}_{4}^{\prime }$相关联。我们使用同调的计算方法来提供关于 $\mathcal {A}({K}_{4}^\{prime })$ 的有限维尔马模块的所有不可还原商的明确实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.

Computation of the Homology of the Complexes of Finite Verma Modules for \({K}_{4}^{\prime }\)

Abstract