Cohomologies, non-abelian extensions and Wells sequences of lambda-weighted Rota-Baxter Lie coalgebras

2024/01/26 by Qinxiu Sun, Zhen Li, Sun, Qinxiu +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2401.14875

openalex publication_date 2024/01/26 · openalex created_date 2024/01/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate cohomologies and non-abelian extensions of lambda-weighted Rota-Baxter Lie coalgebras. First, we consider Lie comodules and cohomologies of lambda-weighted Rota-Baxter Lie coalgebras. Next, we study non-abelian extensions of lambda-weighted Rota-Baxter Lie coalgebras and classify the non-abelian extensions in terms of non-abelian cohomology group. Furthermore, we explore extensibility of a pair of automorphisms about a non-abelian extension of lambda-weighted Rota-Baxter Lie coalgebras, and derive the fundamental sequences of Wells in the context of lambda-weighted Rota-Baxter Lie coalgebras. Finally, we discuss the previous results in the case of abelian extensions of lambda-weighted Rota-Baxter Lie coalgebras.

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