From Rota–Baxter algebras to pre-Lie algebras

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 ⩽3 and their corresponding pre-Lie algebras.