Journal of Lie Theory 30 (2020), No. 4, 1047--1060
Copyright Heldermann Verlag 2020
Classification of Nilpotent Lie Superalgebras of Multiplier-Rank Less Than or Equal to 2
Wende Liu
School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, P. R. China
wendeliu@ustc.edu.cn
Yanling Zhang
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China
741488940@qq.com
We introduce the notion of (super-)multiplier-ranks for Lie superalgebras and classify all the finite-dimensional nilpotent Lie superalgebras of multiplier-rank less or equal to 2 over an algebraically closed field of characteristic zero. In the process, we also determine the multipliers of Heisenberg Lie superalgebras.
Keywords: Lie superalgebra, multipliers, super-multiplier-rank.
MSC: 17B05, 17B30, 17B56.
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