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Embedding tensors on 3-Hom-Lie algebras

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arxiv 2307.00961 v1 pith:WLSQLHS2 submitted 2023-05-30 math.RA

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keywords algebrasembeddinghom-liecohomologytensortensorsalgebraapplication
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In this paper, we introduce the notion of embedding tensor on 3-Hom-Lie algebras and naturally induce 3-Hom-Leibniz algebras. Moreover, the cohomology theory of embedding tensors on 3-Hom-Lie algebras is defined. As an application, we show that if two linear deformations of an embedding tensor on a 3-Hom-Lie algebra are equivalent, then their infinitesimals belong to the same cohomology class in the first cohomology group.

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