W(2)到Kac模的0阶上同调

丁亚洲; 王淑娟

doi:10.3969/j.issn.1000-1565.2022.06.002

河北大学学报(自然科学版) >

2022 , Vol. 42 >Issue 6: 565 - 568

DOI: https://doi.org/10.3969/j.issn.1000-1565.2022.06.002

W(2)到Kac模的0阶上同调

丁亚洲 ,
王淑娟

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丁亚洲(1995—),男,河南驻马店人,黑龙江大学在读硕士研究生,主要从事李理论方向研究.
E-mail:dingyazhou215@163.com

收稿日期: 2022-03-22

网络出版日期: 2023-02-22

基金资助

国家自然科学基金资助项目(12061029);黑龙江省自然科学基金资助项目(YQ2020A005)

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Zeroth cohomology from W(2)to Kac modules

DING Yazhou ,
WANG Shujuan

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1. School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China; (2. College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China

Received date: 2022-03-22

Online published: 2023-02-22

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摘要

确定了特征p≥3的域上Witt型模李超代数W(2)到所有限制以及非限制Kac模K_S(λ)的0阶上同调.得出以下结论:当S=0,λ=(0,2)时,W(2)到限制Kac模K_S(λ)的0阶上同调空间是一维的;否则,W(2)到Kac模K_S(λ)的0阶上同调空间都是零维的.

关键词： Witt型模李超代数W(2); Kac模; 上同调

本文引用格式

丁亚洲 , 王淑娟 . W(2)到Kac模的0阶上同调[J]. 河北大学学报(自然科学版), 2022 , 42(6) : 565 -568 . DOI: 10.3969/j.issn.1000-1565.2022.06.002

Abstract

Over a field of characteristic p≥3,this paper determines the 0-th cohomology from Witt-type Modular Lie superalgebra W(2)to all restricted and non-restricted Kac modules K_S(λ).We show that the 0-th cohomology spaces of W(2)with coefficients in K_S(λ)is 1-dimensional if S=0, λ=(0,2),and the 0-th cohomology spaces of W(2)with coefficients in K_S(λ)is 0-dimensional if S≠0 or λ≠(0,2).

Key words： Witt-type modular Lie superalgebra; Kac module; cohomology

参考文献

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