On Kac–Weisfeiler modules for general and special linear lie superalgebras

Yang Zeng; Bin Shu

doi:10.1007/s11856-016-1338-1

On Kac–Weisfeiler modules for general and special linear lie superalgebras

Yang Zeng^*
, Bin Shu

^*此作品的通讯作者

数学科学学院

Nanjing Audit University

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

Let g:= gl_m|_n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for gl_m|_n. We also establish the corresponding consequence for the special linear Lie superalgebra sl_m|_n with the restrictions that p > 2 and p ∤ (m - n).

源语言	英语
页（从-至）	471-490
页数	20
期刊	Israel Journal of Mathematics
卷	214
期	1
DOI	https://doi.org/10.1007/s11856-016-1338-1
出版状态	已出版 - 1 7月 2016

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abstract = "Let g:= glm|n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac{\textendash}Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac{\textendash}Weisfeiler property presented by Wang{\textendash}Zhao in [9]. In this paper, we verify the existence of the Kac{\textendash}Weisfeiler modules for glm|n. We also establish the corresponding consequence for the special linear Lie superalgebra slm|n with the restrictions that p > 2 and p ∤ (m - n).",

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N2 - Let g:= glm|n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for glm|n. We also establish the corresponding consequence for the special linear Lie superalgebra slm|n with the restrictions that p > 2 and p ∤ (m - n).

AB - Let g:= glm|n be a general linear Lie superalgebra over an algebraically closed field (Formula Presented) of characteristic p > 2. A module of g is said to be of Kac–Weisfeiler type if its dimension coincides with the dimensional lower bound in the super Kac–Weisfeiler property presented by Wang–Zhao in [9]. In this paper, we verify the existence of the Kac–Weisfeiler modules for glm|n. We also establish the corresponding consequence for the special linear Lie superalgebra slm|n with the restrictions that p > 2 and p ∤ (m - n).

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On Kac–Weisfeiler modules for general and special linear lie superalgebras

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