On multipliers of pairs of Lie superalgebras

Abstract

In this article, we study the notion of the Schur multiplier $\mathcal{M}(N,L)$ of a pair $(N,L)$ of Lie superalgebras and obtain some upper bounds concerning dimensions. Moreover, we characterize the pairs of finite dimensional (nilpotent) Lie superalgebras for which $\dim \mathcal{M}(N,L)= \frac{1}{2}\big{(}(m+n)^2+(n-m)\big{)}+\dim N\dim(L/N)-t$, for $t=0,1$, where $\dim N=(m|n)$.

References in corpus (3)

• Non-abelian tensor product and homology of Lie Superalgebras
• Cohomology of Heisenberg Lie Superalgebras
• Classification of nilpotent Lie superalgebras of multiplier-rank $\le 2$

Cited by in corpus (1)

• The Schur multiplier of an $n$-Lie superalgebra