From Rota-Baxter Algebras to Pre-Lie Algebras

TL;DR

This paper classifies all Rota-Baxter operators of weight 1 on low-dimensional complex associative algebras and explores their induced pre-Lie algebra structures, connecting algebraic operators to geometric algebraic structures.

Contribution

It provides a complete classification of Rota-Baxter operators of weight 1 on complex associative algebras of dimension up to 3 and describes the resulting pre-Lie algebras.

Findings

Classified all Rota-Baxter operators of weight 1 in dimension ≤ 3

Identified corresponding pre-Lie algebra structures

Established connections between associative and pre-Lie algebras

Abstract

Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension $\leq 3$ and their corresponding pre-Lie algebras.