Deformations and generalized derivations of Hom-Lie conformal algebras

TL;DR

This paper extends cohomology and derivation theories to Hom-Lie conformal algebras, exploring their deformations and introducing new derivation concepts to deepen understanding of their structure.

Contribution

It develops the cohomology theory for Hom-Lie conformal algebras and introduces $ extalpha^k$-derivations, advancing the study of their deformations and structural properties.

Findings

Established cohomology framework for Hom-Lie conformal algebras

Analyzed properties of $ extalpha^k$-derivations

Applied theory to deformations of regular Hom-Lie conformal algebras

Abstract

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce $\alpha^k$-derivations of multiplicative Hom-Lie conformal algebras and study their properties.