Multipliers, covers, and stem extensions for Lie superalgebras

doi:10.1007/s11464-021-0907-8

Front. Math. China

2021, Vol. 16

Issue (4) : 979-995 https://doi.org/10.1007/s11464-021-0907-8

RESEARCH ARTICLE

Multipliers, covers, and stem extensions for Lie superalgebras

Wende LIU¹, Xingxue MIAO²(

)

¹. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
². School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China

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Abstract

Suppose that the underlying field is of characteristic different from 2 and 3. We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L; up to equivalence of extensions. Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms. Finally, we describe the multipliers, covers, and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.

Keywords Multiplier cover stem extension Heisenberg superalgebra filiform Lie supleralgebra

Corresponding Author(s): Xingxue MIAO

Issue Date: 11 October 2021

Cite this article:

Wende LIU,Xingxue MIAO. Multipliers, covers, and stem extensions for Lie superalgebras[J]. Front. Math. China, 2021, 16(4): 979-995.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0907-8
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I4/979

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