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.

arXiv comment23 pages, appear in Journal of Physics A; Mathematical and Theoretical

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• Rota-Baxter Operators on Quadratic Algebras
• Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras
• Rota-Baxter operators on a sum of fields
• Construction of Rota-Baxter algebras via Hopf module algebras
• Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras and polynomial algebras
• Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
• Quasi-idempotent Rota-Baxter operators arising from quasi-idempotent elements
• Rota-Baxter operators of nonzero weight on the split Cayley-Dickson algebra
• Burde's series of simple pre-Lie algebras
• Rota-Baxter operators of nonzero weight on the matrix algebra of order three
• Double Lie algebras of a nonzero weight
• Kupershmidt-Nijenhuis structures on pre-Malcev algebras
• An operator approach to the rational solutions of the classical Yang-Baxter equation