We consider Lie algebras equipped with a Rota Baxter operator. The forgetful functor from this category to the category of Lie algebras has a left adjoint one denoted by U-RB. We prove an operator analogue of the Poincare-Birkhoff-Witt theorem for U-RB by means of Grobner-Shirshov bases theory for Lie algebras with an additional operator.
|Number of pages||19|
|Journal||Journal of Lie Theory|
|Publication status||Published - 2017|
- Rota-Baxter operator
- free Lie algebra
- universal envelope
- DENDRIFORM ALGEBRAS