From Rota-Baxter Algebras to Pre-Lie Algebras
arXiv:0711.1389 · doi:10.1088/1751-8113/41/1/015201
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.
23 pages, appear in Journal of Physics A; Mathematical and Theoretical