Journal of Lie Theory 31 (2021), No. 1, 221--232
Copyright Heldermann Verlag 2021
Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras
Wende Liu
School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
wendeliu@ustc.edu.cn
Yong Yang
School of Mathematics, Jilin University, Changchun 130012, P. R. China
and: Institute of Physics, University of Pécs, 7622 Hungary
yangyong195888221@163.com
Xiankun Du
School of Mathematics, Jilin University, Changchun 130012, P. R. China
duxk@jlu.edu.cn
We study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an application, we prove that the cup product over the adjoint cohomology superspaces for Heisenberg Lie superalgebras is trivial and we also determine the adjoint Betti numbers for Heisenberg Lie superalgebras by means of Hochschild-Serre spectral sequences.
Keywords: Nilpotent Lie superalgebra, cup product, Betti number, spectral sequence.
MSC: 17B30, 17B56.
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