Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 887-905 |
Number of pages | 19 |
Journal | Journal of Lie Theory |
Volume | 27 |
Issue number | 3 |
Publication status | Published - 2017 |
Keywords
- Rota-Baxter operator
- free Lie algebra
- universal envelope
- DENDRIFORM ALGEBRAS
- BASES
- SYSTEMS