Groebner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra

Abstract

Consider the class RBLie of Lie algebras equipped with a Rota---Baxter operator. Then the forgetful functor RBLie --> Lie has a left adjoint one denoted by $U_{RB}(\cdot )$. We prove an "operator" analogue of the Poincare---Birkhoff---Witt theorem for $U_{RB}(L)$, where $L$ is an arbitrary Lie algebra, by means of Gröbner---Shirshov bases theory for Lie algebras with an additional operator.

16 pages

References in corpus (1)

• Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases

Cited by in corpus (4)

• Universal enveloping Rota-Baxter algebras of preassociative and postassociative algebras
• Universal enveloping Lie Rota-Baxter algebra of preLie and post-Lie algebras
• Embedding of post-Lie algebras into postassociative algebras
• Free differential Lie Rota-Baxter algebras and Gröbner-Shirshov bases