Geodesic
Extending Structures of Rota-Baxter Lie Algebras
Journal of Lie theory, Tome 34 (2024) no. 4, pp. 753-772
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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.
Classification : 17B38, 17B05, 17B60
Mots-clés : Rota-Baxter Lie algebras, extending structures, crossed products, factorization problems 
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     author = {X. Peng and Y. Zhang},
     title = {Extending {Structures} of {Rota-Baxter} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {753--772},
     year = {2024},
     volume = {34},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2024_34_4_JLT_2024_34_4_a0/}
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X. Peng; Y. Zhang. Extending Structures of Rota-Baxter Lie Algebras. Journal of Lie theory, Tome 34 (2024) no. 4, pp. 753-772. http://geodesic.mathdoc.fr/item/JLT_2024_34_4_JLT_2024_34_4_a0/