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 URB. We prove an operator analogue of the Poincaré-Birkhoff-Witt theorem for URB by means of Gröbner-Shirshov bases theory for Lie algebras with an additional operator.
|Number of pages||19|
|Journal||Journal of Lie Theory|
|Publication status||Published - 1 Jan 2017|
- Free Lie algebra
- Rota-Baxter operator
- Universal envelope