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 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.
Original language | English |
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Pages (from-to) | 887-905 |
Number of pages | 19 |
Journal | Journal of Lie Theory |
Volume | 27 |
Issue number | 3 |
Publication status | Published - 1 Jan 2017 |
Keywords
- Free Lie algebra
- Rota-Baxter operator
- Universal envelope