This research investigates cohomologies in modified Rota-Baxter Lie triple systems, suggesting new applications.
In this paper, we consider modified Rota-Baxter Lie triple systems with higher derivations. A pair consisting of a modified Rota-Baxter Lie triple system and a higher derivation is called a modified Rota-Baxter LieTHDer pair. We investigate cohomologies of modified Rota-Baxter LieTHDer pairs with coefficients in a suitable representation. As applications, we study abelian extensions and formal one-parameter deformations of modified Rota-Baxter LieTHDer pairs.
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Ke et al. (2025) studied this question.
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