Abstract
A Lie superalgebra H satisfying is called generalized Heisenberg Lie superalgebra. If is the minimum number of generators required to describe H, then in this article we intend to find the structure of H when precisely . Further, we give some results about the capability, and the Schur multiplier of H. Moreover, we find multiplier for any nilpotent Lie superalgebra L of nilpotency class 2 with when its derived subalgebra is of maximum possible dimension and finally show that such an algebra is capable.
2010 Mathematics subject classifications:
Acknowledgments
We would like to thank K. C. Pati for his encouragement. We are also grateful to the referee for his/her helpful corrections which improved the presentation of this paper. S. Nayak is supported by NBHM Post Doctoral Fellowship, Govt. of India.
Disclosure statement
No potential conflict of interest was reported by the author(s).