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Cohomology of weighted Rota-Baxter Lie algebras and Rota-Baxter paired operators
Published 5 Sep 2021 in math.RT and math.RA | (2109.01972v1)
Abstract: In this paper, we define representations and cohomology of weighted Rota-Baxter Lie algebras. As applications of cohomology, we study abelian extensions and formal $1$-parameter deformations weighted Rota-Baxter Lie algebras. Finally, we consider weighted Rota-Baxter paired operators that induces a weighted Rota-Baxter Lie algebra and a representation of it. We define suitable cohomology for such paired operators that govern deformation.
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