On multipliers of pairs of Lie superalgebras

Abstract

In this article, we study the notion of the Schur multiplier 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 M(N, L) = 1 2 (m + n) 2 + (n − m) + dim N dim(L/N) − t, for t = 0, 1, where dim N = (m|n).