Journal of Hebei University(Natural Science Edition) >

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

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

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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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 KS(λ).We show that the 0-th cohomology spaces of W(2)with coefficients in KS(λ)is 1-dimensional if S=0, λ=(0,2),and the 0-th cohomology spaces of W(2)with coefficients in KS(λ)is 0-dimensional if S≠0 or λ≠(0,2).

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

Cite this article

DING Yazhou , WANG Shujuan . Zeroth cohomology from W(2)to Kac modules[J]. Journal of Hebei University(Natural Science Edition), 2022 , 42(6) : 565 -568 . DOI: 10.3969/j.issn.1000-1565.2022.06.002

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