Journal of Lie Theory

no. 1
Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 221-232
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.
DOI: 10.5802/jolt.1166
Classification: 17B30, 17B56
Keywords: Nilpotent Lie superalgebra, cup product, Betti number, spectral sequence 
@article{JOLT_2021_31_1_a10,
     author = {W. Liu and Y. Yang and X. Du},
     title = {Adjoint {Cohomology} of {Two-Step} {Nilpotent} {Lie} {Superalgebras}},
     journal = {Journal of Lie Theory},
     pages = {221--232},
     year = {2021},
     volume = {31},
     number = {1},
     doi = {10.5802/jolt.1166},
     zbl = {1478.17012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1166/}
}
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W. Liu; Y. Yang; X. Du. Adjoint Cohomology of Two-Step Nilpotent Lie Superalgebras. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 221-232. doi: 10.5802/jolt.1166

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