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Volume 35, Issue 1
Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

Yongsheng Cheng, Linli Wu & Panyin Wang

DOI: 10.13447/j.1674-5647.2019.01.09

Commun. Math. Res., 35 (2019), pp. 81-96.

Published online: 2019-12

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  • 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.

  • Keywords

Rota-Baxter operators, 3-dimensional Lie algebra, classical Yang-Baxter equation, left-symmetric algebra

  • AMS Subject Headings

17B10, 17B65, 17B68

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yscheng@henu.edu.cn (Yongsheng Cheng)

  • BibTex
  • RIS
  • TXT
@Article{CMR-35-81, author = {Cheng , YongshengWu , Linli and Wang , Panyin}, title = {Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {1}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.01.09}, url = {http://global-sci.org/intro/article_detail/cmr/13477.html} }
TY - JOUR T1 - Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation AU - Cheng , Yongsheng AU - Wu , Linli AU - Wang , Panyin JO - Communications in Mathematical Research VL - 1 SP - 81 EP - 96 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.01.09 UR - https://global-sci.org/intro/article_detail/cmr/13477.html KW - Rota-Baxter operators, 3-dimensional Lie algebra, classical Yang-Baxter equation, left-symmetric algebra AB -

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.

Cheng , YongshengWu , Linli and Wang , Panyin. (2019). Rota-Baxter Operators on 3-Dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation. Communications in Mathematical Research . 35 (1). 81-96. doi:10.13447/j.1674-5647.2019.01.09
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