1. Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms.
- Author
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Mishra, Satyendra Kumar, Das, Apurba, and Hazra, Samir Kumar
- Subjects
- *
LIE algebras , *AUTOMORPHISMS , *COHOMOLOGY theory - Abstract
A Rota-Baxter Lie algebra g T is a Lie algebra g equipped with a Rota-Baxter operator T : g → g. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra g T by another Rota-Baxter Lie algebra h S. We define the non-abelian cohomology H n a b 2 (g T , h S) which classifies equivalence classes of such extensions. Given a non-abelian extension [Display omitted] of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of Rota-Baxter automorphisms in Aut (h S) × Aut (g T) to be induced by an automorphism in Aut (e U) lies in the cohomology group H n a b 2 (g T , h S). As a byproduct, we obtain the Wells short-exact sequence in the context of Rota-Baxter Lie algebras. Finally, we show how these results fit with abelian extensions of Rota-Baxter Lie algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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