Cohomologies, non-abelian extensions and Wells sequences of lambda-weighted Rota-Baxter Lie coalgebras
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.
Keywords
Cite
@article{arxiv.2401.14875,
title = {Cohomologies, non-abelian extensions and Wells sequences of lambda-weighted Rota-Baxter Lie coalgebras},
author = {Qinxiu Sun and Zhen Li},
journal= {arXiv preprint arXiv:2401.14875},
year = {2024}
}