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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

Yanling Zhang
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, P. R. China

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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