On the isomorphism of non-abelian extensions of n-Lie algebras

In this paper, we introduce the notion of a derivation of a regular Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions of regular Hom-Lie algebras. We show that isomorphism classes of diagonal non-abelian extensions of a regular Hom-Lie algebra [Formula: see text] by a regular Hom-Lie algebra [Formula: see text] are in one-to-one correspondence with homotopy classes of morphisms from [Formula: see text] to the derivation Hom-Lie 2-algebra [Formula: see text].

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Representations and deformations of 3-Hom-ρ-Lie algebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498823500640 ◽

2021 ◽

Author(s):

Esmaeil Peyghan ◽

Aydin Gezer ◽

Zahra Bagheri ◽

Inci Gultekin

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Abelian Extension ◽

Abelian Extensions ◽

Definition Of

The aim of this paper is to introduce 3-Hom-[Formula: see text]-Lie algebra structures generalizing the algebras of 3-Hom-Lie algebra. Also, we investigate the representations and deformations theory of this type of Hom-Lie algebras. Moreover, we introduce the definition of extensions and abelian extensions of 3-Hom-[Formula: see text]-Lie algebras and show that associated to any abelian extension, there is a representation and a 2-cocycle.

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Cohomology, derivations and abelian extensions of 3-Lie algebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498819501305 ◽

2019 ◽

Vol 18 (07) ◽

pp. 1950130 ◽

Cited By ~ 1

Author(s):

Senrong Xu

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Representation Formula ◽

Abelian Extension ◽

Abelian Extensions ◽

First Order

Given a representation [Formula: see text] of a 3-Lie algebra [Formula: see text], we construct first-order cohomology classes by using derivations of [Formula: see text], [Formula: see text] and obtain a Lie algebra [Formula: see text] with a representation [Formula: see text] on [Formula: see text]. In the case that [Formula: see text] is given by an abelian extension [Formula: see text] of 3-Lie algebras with [Formula: see text], we obtain obstruction classes for extensibility of derivations of [Formula: see text] and [Formula: see text] to those of [Formula: see text]. An application of the representation [Formula: see text] to derivations is also discussed.

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