Journal of Lie Theory 34 (2024), No. 4, 753--772
Copyright Heldermann Verlag 2024
Extending Structures of Rota-Baxter Lie Algebras
Xiaosong Peng
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, P.R. China
pengxiaosong3@163.com
Yi Zhang
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, P.R. China
zhangy2016@nuist.edu.cn
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.
Keywords: Rota-Baxter Lie algebras, extending structures, crossed products, factorization problems.
MSC: 17B38, 17B05, 17B60.
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