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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 6128102, 7 pages
https://doi.org/10.1155/2017/6128102
Research Article

Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical -Matrices

School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

Correspondence should be addressed to Yongsheng Cheng; nc.ude.uneh@gnehcsy

Received 6 September 2017; Accepted 27 November 2017; Published 18 December 2017

Academic Editor: Boris G. Konopelchenko

Copyright © 2017 Linli Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Our aim is to classify the Rota-Baxter operators of weight 0 on the 3-dimensional Lie algebra whose derived algebra’s dimension is 2. We explicitly determine all Rota-Baxter operators (of weight zero) on the 3-dimensional Lie algebras . Furthermore, we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras and the induced left-symmetry algebra structures on .