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Register a new userAdjoint cohomology of two-step nilpotent Lie superalgebras
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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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Suppose the ground field to be algebraically closed and of characteristic different from $2$ and $3$. All Heisenberg Lie superalgebras consist of two sup
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