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

Vsevolod Gubarev, Pavel Kolesnikov

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)887-905
Number of pages19
JournalJournal of Lie Theory
Volume27
Issue number3
Publication statusPublished - 1 Jan 2017

Keywords

  • Free Lie algebra
  • Rota-Baxter operator
  • Universal envelope

Fingerprint Dive into the research topics of 'Gröbner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra'. Together they form a unique fingerprint.

Cite this