Geodesic
Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras
W. Liu ; Y. Yang ; X. Du
Journal of Lie theory, Tome 31 (2021) no. 1, pp. 221-232
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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.
Classification : 17B30, 17B56
Mots-clés : Nilpotent Lie superalgebra, cup product, Betti number, spectral sequence 
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     title = {Adjoint {Cohomology} of {Two-Step} {Nilpotent} {Lie} {Superalgebras}},
     journal = {Journal of Lie theory},
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     year = {2021},
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W. Liu; Y. Yang; X. Du. Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras. Journal of Lie theory, Tome 31 (2021) no. 1, pp. 221-232. http://geodesic.mathdoc.fr/item/JLT_2021_31_1_JLT_2021_31_1_a10/