Journal of Lie Theory

no. 4
Extending Structures of Rota-Baxter Lie Algebras
Xiaosong Peng1; Yi Zhang2
1School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, P.R. China
2School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, P.R. China
Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 753-772
We first introduce the notion of an extending datum of a Rota-Baxter Lie algebra through a vector space. We then construct a unified product for the Rota-Baxter Lie algebra with a vector space as a main ingredient in our approach. Finally, we solve the extending structures problem of Rota-Baxter Lie algebras, which generalizes and unifies two problems in the study of Rota-Baxter Lie algebras: the extension problem studied by Mishra-Das-Hazra and the factorization problem investigated by Lang-Sheng.
DOI: 10.5802/jolt.1359
Classification: 17B38, 17B05, 17B60
Keywords: Rota-Baxter Lie algebras, extending structures, crossed products, factorization problems

Xiaosong Peng  1 ; Yi Zhang  2

1 School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, P.R. China
2 School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, P.R. China 
Xiaosong Peng; Yi Zhang. Extending Structures of Rota-Baxter Lie Algebras. Journal of Lie Theory, Volume 34 (2024) no. 4, pp. 753-772. doi: 10.5802/jolt.1359
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