Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation
Year: 2019
Author: Yongsheng Cheng, Linli Wu, Panyin Wang
Communications in Mathematical Research , Vol. 35 (2019), Iss. 1 : pp. 81–96
Abstract
In this paper, we compute Rota-Baxter operators on the 3-dimensional Lie algebra $g$ whose derived algebra's dimension is 2. Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras $g\ltimes_{ad^*}g^*$ and some new structures of left-symmetric algebra induced from $g$ and its Rota-Baxter operators.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2019.01.09
Communications in Mathematical Research , Vol. 35 (2019), Iss. 1 : pp. 81–96
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Rota-Baxter operators 3-dimensional Lie algebra classical Yang-Baxter equation left-symmetric algebra