A Poincar\'{e}-Birkhoff-Witt theorem for the universal enveloping algebra of a Rota-Baxter Lie algebra
Quantum Algebra
2022-10-25 v2 Rings and Algebras
Abstract
Rota-Baxter associative algebras and Rota-Baxter Lie algebras are both important in mathematics and mathematical physics, with the former a basic structure in quantum field renormalization and the latter a operator form of the classical Yang-Baxter equation. An outstanding problem posed by Gubarev is to determine whether there is a Poincar\'e-Birkhoff-Witt theorem for the universal enveloping Rota-Baxter associative algebra of a Rota-Baxter Lie algebra. This paper resolves this problem positively, working with operated algebras and applying the method of Gr\"obner-Shirshov bases.
Keywords
Cite
@article{arxiv.2209.03559,
title = {A Poincar\'{e}-Birkhoff-Witt theorem for the universal enveloping algebra of a Rota-Baxter Lie algebra},
author = {Zhi-Cheng Zhu and Xing Gao and Li Guo and Jun Pei},
journal= {arXiv preprint arXiv:2209.03559},
year = {2022}
}
Comments
There was an error in considering all the compositions in Sec 3.1