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

Wen Teng; Xiansheng Dai; Wen Teng; Xiansheng Dai

doi:10.3934/era.2025063

Electronic Research Archive

2025, Volume 33, Issue 3: 1367-1383. doi: 10.3934/era.2025063

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Research article

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

Wen Teng ^{1
,
,},
Xiansheng Dai ²

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
2.
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Received: 21 November 2024 Revised: 20 February 2025 Accepted: 28 February 2025 Published: 10 March 2025

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.
- 3-Lie algebra,
- nonabelian embedding tensor,
- 3-Leibniz algebra,
- 3-Leibniz-Lie algebra,
- cohomology,
- infinitesimal deformation
Citation: Wen Teng, Xiansheng Dai. Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras[J]. Electronic Research Archive, 2025, 33(3): 1367-1383. doi: 10.3934/era.2025063

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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.

References

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