@article{Xu2024, 
author = {Senrong Xu and Wei Wang and Jia Zhao},
title = {Twisted Rota-Baxter operators on Hom-Lie algebras},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {2619-2640},
keywords = {twisted Rota-Baxter operators, Hom-Lie algebra s, Maurer-Cartan elements, L∞-algebras, cohomologies, deformations},
url = {https://www.sciopen.com/article/10.3934/math.2024129},
doi = {10.3934/math.2024129},
abstract = {Uchino initiated the investigation of twisted Rota-Baxter operators on associative algebras. Relevant studies have been extensive in recent times. In this paper, we introduce the notion of a twisted Rota-Baxter operator on a Hom-Lie algebra. By utilizing higher derived brackets, we establish an explicit        L          ∞      -algebra whose Maurer-Cartan elements are precisely twisted Rota-Baxter operators on Hom-Lie algebra s. Additionally, we employ Getzler's technique of twisting        L    ∞  -algebras to establish the cohomology of twisted Rota-Baxter operators. We demonstrate that this cohomology can be regarded as the Chevalley-Eilenberg cohomology of a specific Hom-Lie algebra with coefficients in an appropriate representation. Finally, we study the linear and formal deformations of twisted Rota-Baxter operators by using the cohomology defined above. We also show that the rigidity of a twisted Rota-Baxter operator can be derived from Nijenhuis elements associated with a Hom-Lie algebra.}
}