@article{Teng2023, 
author = {Wen Teng and Jiulin Jin and Yu Zhang},
title = {Cohomology of nonabelian embedding tensors on Hom-Lie algebras},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {21176-21190},
keywords = {Hom-Lie algebra, Hom-Leibniz-Lie algebra, nonabelian embedding tensor, cohomology, deformation},
url = {https://www.sciopen.com/article/10.3934/math.20231079},
doi = {10.3934/math.20231079},
abstract = {In this paper, we generalize known results of nonabelian embedding tensor to the Hom setting. We introduce the concept of Hom-Leibniz-Lie algebra, which is the basic algebraic structure of nonabelian embedded tensors on Hom-Lie algebras and can also be regarded as a nonabelian generalization of Hom-Leibniz algebra. Moreover, we define a cohomology of nonabelian embedding tensors on Hom-Lie algebras with coefficients in a suitable representation. The first cohomology group is used to describe infinitesimal deformations as an application. In addition, Nijenhuis elements are used to describe trivial infinitesimal deformations.}
}