Some Studies On Central Derivation of Nilpotent Lie Superalgebras

TL;DR

This paper extends the study of central derivations from nilpotent Lie algebras to Lie superalgebras, focusing on isoclinism and nilpotency, with implications for mathematical physics.

Contribution

It introduces and explores the concept of isoclinism in Lie superalgebras, extending previous results from Lie algebras to this broader class.

Findings

Extended central derivation results to Lie superalgebras

Analyzed isoclinism in the context of nilpotent Lie superalgebras

Provided new insights into the structure of nilpotent Lie superalgebras

Abstract

Many theorems and formulas of Lie algebras run quite parallel to Lie superalgebra case, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case, as these type of algebras have wide applications in physics and related theories. Using the concept of isoclinism, F. Saeedi and S. Sheikh-Mohseni recently studied the central derivation of nilpotent Lie algebra with nilindex 2. The purpose of the present paper is to continue and extend the investigation to obtain some similar results for Lie superalgebras, as isoclinism in Lie superalgebra is being recently introduced.