Rota-Baxter family $\Omega$-associative conformal algebras and their cohomology theory

TL;DR

This paper introduces Rota-Baxter family $\,\, ext{ extOmega} ext{-associative conformal algebras} and develops their cohomology theory, linking lower degree cohomology groups to formal deformations.

Contribution

It proposes a new class of conformal algebras and establishes their cohomology framework, extending the understanding of algebraic deformations.

Findings

Defined Rota-Baxter family $ extOmega$-associative conformal algebras

Developed cohomology theory for these algebras

Connected cohomology groups to formal deformation theory

Abstract

In this paper, we first propose the concept of Rota-Baxter family $\Omega$-associative conformal algebras, then we study the cohomology theory of Rota-Baxter family $\Omega$-associative conformal algebras of any weight and justify it by interpreting the lower degree cohomology groups as formal deformations.