Multipliers of nilpotent Lie superalgebras

Abstract

In this paper, first we prove that all finite dimensional special Heisenberg Lie superalgebras with even center have same dimension, say (2m + 1 | n) for some non-negative integers m, n and are isomorphism with them. Further, for a nilpotent Lie superalgebra, where M(L) denotes the Schur multiplier of L. Moreover, if (r, s) = (1, 0) (respectively (r, s) = (0, 1)), then the equality holds if and only if L ∼ = H(1, 0) ⊕ A1 (respectively H(0, 1) ⊕ A2), where A1 and A2 are abelian Lie superalgebras with dim and H(1, 0), H(0, 1) are special Heisenberg Lie superalgebras of dimension 3 and 2 respectively.

Multipliers, Covers and Stem Extensions for Lie Superalgebras

“…In [10,Proposition 4.4] (see also [13,Theorem 4.3]), the authors characterize the multipliers of Heisenberg superalgebras of even center:…”

The multiplier and cohomology of Lie superalgebras

“…One might find various bounds of the dimension of the multipliers of nilpotent Lie algebras [11][12][13][14][15][16]. S. Nayak generalized the definition of multipliers and covers of Lie algebras to Lie superalgebras case and introduced the concepts of isoclinism in Lie superalgebras [17,18]. Y. L. Zhang and W. D. Liu introduced the concept of (super-)multiplier-rank for Lie superalgeras and classified the nilpotent Lie superalgebras of multiplier-rank ≤ 2 [19].…”