Adjoint cohomology of two-step nilpotent Lie superalgebras
Wende Liu, Yong Yang, and Xiankun Du
TL;DR
This paper investigates the structure of the cohomology of two-step nilpotent Lie superalgebras, focusing on cup products and Betti numbers, with specific results for Heisenberg Lie superalgebras.
Contribution
It provides new insights into the cohomology ring structure and Betti numbers of two-step nilpotent Lie superalgebras, especially demonstrating the triviality of cup products in certain cases.
Findings
Cup product over adjoint cohomology of Heisenberg Lie superalgebras is trivial.
Determined the adjoint Betti numbers for Heisenberg Lie superalgebras.
Analyzed cohomology superspaces using Hochschild-Serre spectral sequences.
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons