On 2-nilpotent multiplier of Lie superalgebras

Abstract

In this article, we define the c-nilpotent multiplier of a finite dimensional Lie superalgebra. We characterize the structure of 2-nilpotent multiplier of finite dimensional nilpotent Lie superalgebras whose derived subalgebras have dimension at most one. Then we give an upper bound on the dimension of 2-nilpotent multiplier of any finite dimensional nilpotent Lie superalgebra. Moreover, we discuses the 2-capability of special as well as odd Heisenberg Lie superalgebras and abelian Lie superalgebras.