
Journal of Lie Theory 31 (2021), No. 1, 221232 Copyright Heldermann Verlag 2021 Adjoint Cohomology of TwoStep Nilpotent Lie Superalgebras Wende Liu School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China wendeliu@ustc.edu.cn Yong Yang School of Mathematics, Jilin University, Changchun 130012, P. R. China and: Institute of Physics, University of Pécs, 7622 Hungary yangyong195888221@163.com Xiankun Du School of Mathematics, Jilin University, Changchun 130012, P. R. China duxk@jlu.edu.cn We study the cup products and Betti numbers over cohomology superspaces of twostep 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 HochschildSerre spectral sequences. Keywords: Nilpotent Lie superalgebra, cup product, Betti number, spectral sequence. MSC: 17B30, 17B56. [ Fulltextpdf (125 KB)] for subscribers only. 