
TL;DR
This paper investigates the Schur multiplier of pairs of Lie superalgebras, providing upper bounds on their dimensions and characterizing specific finite-dimensional nilpotent pairs with precise multiplier dimensions.
Contribution
It introduces new bounds on the Schur multiplier of Lie superalgebra pairs and characterizes cases where the dimension attains a specific formula.
Findings
Derived upper bounds for the dimension of the Schur multiplier.
Characterized pairs of finite-dimensional nilpotent Lie superalgebras with specific multiplier dimensions.
Provided explicit formulas for special cases with t=0,1.
Abstract
In this article, we study the notion of the Schur multiplier of a pair 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 , where .
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