Restricted Cohomology of Restricted Lie Superalgebras

Suppose the ground field F is an algebraically closed field characteristic of p > 2. In this paper, we investigate the restricted cohomology theory of restricted Lie superalgebras. Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given. We show...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2022-11, Vol.38 (11), p.2115-2130
Main Authors: Yuan, Ji Xia, Chen, Liang Yun, Cao, Yan
Format: Article
Language:English
Subjects:
Algebra
Homology
Lie groups
Mathematics
Mathematics and Statistics
Modules
Supersymmetry
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Summary:Suppose the ground field F is an algebraically closed field characteristic of p > 2. In this paper, we investigate the restricted cohomology theory of restricted Lie superalgebras. Algebraic interpretations of low dimensional restricted cohomology of restricted Lie superalgebra are given. We show that there is a family of restricted model filiform Lie superalgebra L p , p λ structures parameterized by elements λ ∈ F p . We explicitly describe both the 1-dimensional ordinary and restricted cohomology superspaces of L p , p λ with coefficients in the 1-dimensional trivial module and show that these superspaces are equal. We also describe the 2-dimensional ordinary and restricted cohomology superspaces of L p , p λ with coefficients in the 1-dimensional trivial module and show that these superspaces are unequal.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-022-1088-4