Cohomology of Twisted Rota-Baxter operators on Associative~Conformal Algebra

TL;DR

This paper develops a cohomology theory for twisted Rota-Baxter operators on associative conformal algebras, using $L_$-algebra structures and Hochschild cohomology, and investigates their deformations.

Contribution

It introduces a cohomology framework for twisted Rota-Baxter operators on associative conformal algebras and explores their deformations using $L_$-algebra structures.

Findings

Constructed an $L_$-algebra from Maurer-Cartan elements of twisted Rota-Baxter operators.

Characterized the cohomology as Hochschild cohomology of a specific conformal algebra.

Studied linear and formal deformations of conformal twisted Rota-Baxter operators.

Abstract

In this paper, we examine the concept of twisted Rota-Baxter (TRB) operators on associative conformal algebras. Our strategy begins by constructing an $L_\infty$-algebra using Maurer-Cartan elements derived from $H$-twisted Rota-Baxter ($H$-TRB) operators on associative conformal algebras. This structure leads us to explore the cohomology of the conformal $H$-TRB operator, which is characterized as the Hochschild cohomology of a specific associative conformal algebra with coefficients in a conformal bimodule. Furthermore, we study the linear and formal deformations of conformal $H$-TRB operators to explore the application of cohomology.