@article{Teng2025, 
author = {Wen Teng and Xiansheng Dai},
title = {Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {3},
pages = {1367-1383},
keywords = {3-Lie algebra, nonabelian embedding tensor, 3-Leibniz algebra, 3-Leibniz-Lie algebra, cohomology, infinitesimal deformation},
url = {https://www.sciopen.com/article/10.3934/era.2025063},
doi = {10.3934/era.2025063},
abstract = {The purpose of this paper is to study nonabelian embedding tensors on 3-Lie algebras, and to explore the fundamental algebraic structures, cohomology and deformations associated with them. First, we introduce the concept of nonabelian embedding tensors on 3-Lie algebras. Then, we present the concept of a 3-Leibniz-Lie algebra, which constitutes the fundamental algebraic framework for a nonabelian embedding tensor on a 3-Lie algebra. Additionally, we examine the 3-Leibniz-Lie algebras that are derived from Leibniz-Lie algebras. Finally, we develop the cohomology of nonabelian embedding tensors on 3-Lie algebras and utilize the first cohomology group to characterize infinitesimal deformations.}
}