Isoclinic extensions of Lie algebras

Mohammadzadeh, Hamid; Salemkar, Ali Reza; Riyahi, Zahra

doi:10.3906/mat-1204-7

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“…Eshrati et al [4] studied various properties of isoclinism in n-Lie algebras. Isoclinism of various algebraic structures have been exploid, for more details see [6,7,8,10,12,13,14,15,16,17,11]. Recently in 2020, Arabyani and Sheikh-mohseni [1] introduced the concept of isoclinism on the relative central extensions of pairs of Lie algebras.…”

Section: Introductionmentioning

confidence: 99%

Isoclinic relative extensions of pairs of Lie algebras

Arabyani

Sheikh-Mohseni²

2019

Quaestiones Mathematicae

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In this paper, we show the relation among the relative central extensions in an isoclinism family of a particular relative central extension of Hom-Lie algebras. We define the notion of isoclinism on the central relative extensions of a pair of Hom-Lie algebras. Then, we figure out the concept of isomorphism in the equivalence class of isoclinisms on the central relative extensions of a pair of Hom-Lie algebras.Definition 1.1. A Hom-Lie algebra (L, α L ) is a non-associative algebra L together with a bilinear map [., .] : L × L → L and a linear map α L : L → L satisfying(Hom-Jacobi identity) for all x, y, z ∈ L.

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