Rota-Baxter operators and related structures on anti-flexible algebras

TL;DR

This paper explores the algebraic structures related to Rota-Baxter operators on anti-flexible algebras, including their characterization via graded Lie algebras, deformations, and compatibility conditions.

Contribution

It introduces a graded Lie algebra framework for Rota-Baxter operators, studies their deformations, and defines $\ ext{\ON}$-structures linking compatible Rota-Baxter operators with anti-flexible algebras.

Findings

Constructed a graded Lie algebra characterizing Rota-Baxter operators as Maurer-Cartan elements.

Analyzed infinitesimal deformations of bimodules over anti-flexible algebras.

Defined $\ ext{\ON}$-structures relating compatible Rota-Baxter operators to anti-flexible algebras.

Abstract

In this paper, we first construct a graded Lie algebra which characterizes Rota-Baxter operators on an anti-flexible algebra as Maurer-Cartan elements. Next, we study infinitesimal deformations of bimodules over anti-flexible algebras. We also consider compatible Rota-Baxter operators on bimodules over anti-flexible algebras. Finally, We define $\mathcal{ON}$-structures which give rise to compatible Rota-Baxter operators and vice-versa.