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math.KT2026
Deformations and homotopy theory of Rota-Baxter Lie algebras
Jun Chen, Kai Wang, Guodong Zhou
For Rota-Baxter Lie algebras, a homotopy cooperad is exhibited, whose cobar construction is shown to be the minimal model of the operad of Rota-Baxter Lie algebras by using algebra…
math.KT2026
A Symmetric Counterexample to the Snashall--Solberg Conjecture
Kai Wang, Guodong Zhou
It is shown that the trivial extension of the Xu--Snashall algebra is a symmetric counterexample to the Snashall--Solberg conjecture, which states that the Hochschild cohomology ri…
math.RA2026
Modified Rota-Baxter operators of non-zero weight on -Lie algebras
Shuangjian Guo, Yufei Qin, Guodong Zhou
In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on -Lie algebras and provide some examples. Next, we give various constructions of mo…