6 papers
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…
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…
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…
Deformations of Nijenhuis Lie algebras and Nijenhuis Lie algebroids
Chao Song, Kai Wang, Yuanyuan Zhang +1
This paper is the second in a series dedicated to the operadic study of Nijenhuis structures, focusing on Nijenhuis Lie algebras and Nijenhuis geometry. We introduce the concept of…
Deformation theory and Koszul duality for Rota-Baxter systems
Yufei Qin, Kai Wang, Guodong Zhou
This paper investigates Rota-Baxter systems in the sense of Brzeziński from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equ…
Deformations and homotopy theory of Nijenhuis associative algebras
Chao Song, Kai Wang, Yuanyuan Zhang +1
This paper is the first in a series of works devoted to an operadic study of Nijenhuis structures, focusing on Nijenhuis associative algebras. We introduce the concept of homotopy…