From Rota-Baxter Algebras to 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 $\le 3$ and their corresponding pre-Lie algebras.

23 pages, appear in Journal of Physics A; Mathematical and Theoretical

References in corpus (2)

• Loday-type Algebras and the Rota-Baxter Relation
• Field Algebras

Cited by in corpus (6)

• Rota-Baxter operators on groups
• Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
• Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra
• Burde's series of simple pre-Lie algebras
• Kupershmidt-Nijenhuis structures on pre-Malcev algebras
• Double Lie algebras of a nonzero weight