Extending Structures of Rota-Baxter Lie Algebras

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.