Isoclinism and Relative Central Extensions of a Pair of Lie Superalgebras

Abstract

In the study of Lie algebras and their representation theory, an extension e of a Lie algebra g is an enlargement of g by another Lie algebra h. In particular, central extensions of Lie algebras and Lie superalgebras have been studied ex-tensively by many authors in this field. Recently the concept of relative central extension has been defined for a pair of Lie algebras and Lie superalgebras. In this work, we have shown the relation among the relative central extensions in an isoclinism family of a particular relative central extension. Here, at first we have defined the notion of isoclinism on the relative central extensions of a pair of Lie superalgebras. Then in particular, we have figured out the concept of isomorphism in the equivalence class of isoclinisms on the relative central extensions of a pair of Lie superalgebras.