Abstract
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 A1 is an abelian Lie superalgebra with
and
is a special Heisenberg Lie superalgebra of dimension
.
2010 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgements
The author would like to thank the referee for the useful suggestions. The author would also like to thank Dr. Sudhansu Sekhar Rout for all the fruitful discussions during preparation of the manuscript.