Curved Rota-Baxter systems

TL;DR

This paper introduces curved Rota-Baxter systems, showing how curvature modifies algebraic structures and induces associative and pre-Lie products, with implications for Hochschild cohomology.

Contribution

It extends Rota-Baxter systems by incorporating curvature, demonstrating new algebraic structures and conditions for curved differential graded algebras.

Findings

Curved Rota-Baxter systems induce associative and pre-Lie products.

Under certain conditions, the Hochschild cohomology ring becomes a curved differential graded algebra.

Curvature properties influence the algebraic structures derived from Rota-Baxter systems.

Abstract

Rota-Baxter systems are modified by the inclusion of a curvature term. It is shown that, subject to specific properties of the curvature form, curved Rota-Baxter systems $(A,R,S,\omega)$ induce associative and (left) pre-Lie products on the algebra $A$. It is also shown that if both Rota-Baxter operators coincide with each other and the curvature is $A$-bilinear, then the (modified by $R$) Hochschild cohomology ring over $A$ is a curved differential graded algebra.