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arXiv · 1811.00261

The multiplier and cohomology of Lie superalgebras

Yang Liu·Wende Liu
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Abstract

In this paper, all (super)algebras are over a field $\mathbb{F}$ of characteristic different from $2, 3$. We construct the so-called 5-sequences of cohomology for central extensions of a Lie superalgebra and prove that they are exact. Then we prove that the multipliers of a Lie superalgebra are isomorphic to the second cohomology group with coefficients in the trivial module for the Lie superalgebra under consideration.

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Yang Liu, Wende Liu. 2018-11-01. The multiplier and cohomology of Lie superalgebras. https://arxiv.org/abs/1811.00261

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