Embedding tensors on 3-Hom-Lie algebras

TL;DR

This paper introduces embedding tensors on 3-Hom-Lie algebras, develops their cohomology theory, and explores their deformations, linking algebraic structures with cohomological classifications.

Contribution

It defines embedding tensors on 3-Hom-Lie algebras, induces 3-Hom-Leibniz algebras, and establishes their cohomology theory with applications to deformation equivalence.

Findings

Embedding tensors induce 3-Hom-Leibniz algebras.

Cohomology classifies deformation equivalences.

First cohomology group relates to infinitesimal deformations.

Abstract

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.