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arXiv · 2310.06990

Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras

Wen Teng·Xiansheng Dai
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Abstract

In this paper, first we introduce the notion of a nonabelian embedding tensor on the 3-Lie algebra. Then, we introduce the notion of a 3-Leibniz-Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor on the 3-Lie algebra, and can also be viewed as a nonabelian generalization of a 3-Leibniz algebra. Next we develop the cohomology of nonabelian embedding tensors on 3-Lie algebras with coefficients in a suitable representation and use the first cohomology group to characterize infinitesimal deformations. Finally, we investigate nonabelian embedding tensors on 3-Lie algebras induced by Lie algebras.

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Wen Teng, Xiansheng Dai. 2023-08-16. Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras. https://doi.org/10.3934/era.2025063

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