The cohomology of left-symmetric conformal algebra and its applications

TL;DR

This paper develops a cohomology theory for left-symmetric conformal algebras, establishing an isomorphism with their associated Lie conformal algebras and exploring applications like deformations and extensions.

Contribution

It introduces a cohomology framework for left-symmetric conformal algebras and links it to their Lie counterparts, enabling new insights into their structure and deformations.

Findings

Isomorphism between cohomology spaces of left-symmetric and Lie conformal algebras

Analysis of linear and formal deformations of left-symmetric conformal algebras

Properties of T*-extensions of left-symmetric conformal algebras

Abstract

In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces of the left-symmetric conformal algebra and its sub-adjacent Lie conformal algebra. As applications of the cohomology theory, we study linear deformations, formal $1$-parameter deformations, $T^*$-extensions of a left-symmetric conformal algebra respectively and obtain some properties.