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arXiv · 1809.03150

Adjoint cohomology of two-step nilpotent Lie superalgebras

Wende Liu·Yong Yang·Xiankun Du
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Abstract

In this paper, 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.

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Wende Liu, Yong Yang, Xiankun Du. 2018-09-10. Adjoint cohomology of two-step nilpotent Lie superalgebras. https://arxiv.org/abs/1809.03150

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