论文标题
Poincaré-Birkhoff-Witt定理，用于rota-baxter lie代数的通用包围代数
A Poincaré-Birkhoff-Witt theorem for the universal enveloping algebra of a Rota-Baxter Lie algebra
论文作者
论文摘要
Rota-baxter联想代数和Rota-baxter Lie代数在数学和数学物理学中都很重要，前者是量子场重新归一化的基本结构，而后者是经典Yang-Baxter方程的操作员形式。古巴雷夫（Gubarev）提出的一个杰出问题是确定是否有poincaré-birkhoff-witt定理，用于rota-baxter的通用rota-baxter联合代数为代数。本文与操作的代数合作并应用Gröbner-Shirshov基地的方法可以积极解决此问题。
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 Poincaré-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 Gröbner-Shirshov bases.
