Deformations and generalized derivations of Lie conformal superalgebras

TL;DR

This paper extends the cohomology and derivation theories of Lie conformal superalgebras, introduces generalized derivations, and explores their deformations and structural properties.

Contribution

It develops the cohomology theory for Lie conformal superalgebras and introduces generalized derivations, expanding the understanding of their deformations and algebraic structure.

Findings

Constructed semidirect product of Lie conformal superalgebra and module.

Developed cohomology theory for Lie conformal superalgebras.

Studied properties of generalized derivations.

Abstract

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and its conformal module, and study derivations of this semidirect product. Secondly, we develop cohomology theory of Lie conformal superalgebras and discuss some applications to the study of deformations of Lie conformal superalgebras. Finally, we introduce generalized derivations of Lie conformal superalgebras and study their properties.