Multipliers of nilpotent Lie superalgebras

摘要

In this article, first we prove that all finite dimensional special Heisenberg Lie superalgebras with even center have dimension for some non-negative integers m, n and are isomorphic to H(m, n). Further, for a nilpotent Lie superalgebra L of dimension and with , we find the upper bound , where denotes the Schur multiplier of L. Moreover, if , then the equality holds if and only if where A(1) is an abelian Lie superalgebra with and is a special Heisenberg Lie superalgebra of dimension .