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arXiv · 2302.08725

Deformations and cohomologies of embedding tensors on 3-Lie algebras

Meiyan Hu·Shuai Hou·Lina Song·Yanqiu Zhou
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Abstract

In this paper, first we introduce the notion of an embedding tensor on a 3-Lie algebra, which naturally induces a 3-Leibniz algebra. Using the derived bracket, we construct a Lie 3-algebra, whose Maurer-Cartan elements are embedding tensors. Consequently, we obtain the $L_{\infty}$-algebra that governs deformations of embedding tensors. We define the cohomology theory for embedding tensors on 3-Lie algebras. As applications, we show that if two formal deformations of an embedding tensor on a 3-Lie algebra are equivalent, then their infinitesimals are in the same cohomology class in the second cohomology group. Moreover, an order n deformation of an embedding tensor is extendable if and only if the obstruction class, which is in the third cohomology group, is trivial.

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Meiyan Hu, Shuai Hou, Lina Song, Yanqiu Zhou. 2023-02-17. Deformations and cohomologies of embedding tensors on 3-Lie algebras. https://doi.org/10.1080/00927872.2023.2214215

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