Fuzzy Hom-Lie Ideals of Hom-Lie Algebras

TL;DR

This paper introduces and explores fuzzy Hom-Lie subalgebras and ideals within Hom-Lie algebras, analyzing their properties, relationships, and behavior under morphisms, and constructing new fuzzy subalgebras from finite collections.

Contribution

It defines fuzzy Hom-Lie subalgebras and ideals, studies their properties, and constructs fuzzy subalgebras on direct sums, advancing the understanding of fuzzy structures in Hom-Lie algebras.

Findings

Fuzzy Hom-Lie subalgebras and ideals are characterized and their properties are established.

Relationships between fuzzy and classical Hom-Lie subalgebras and ideals are analyzed.

A method to construct fuzzy Hom-Lie subalgebras on direct sums of finitely many fuzzy subalgebras is developed.

Abstract

In this paper, we introduce the concept of fuzzy Hom-Lie subalgebras (ideals) of Hom-Lie algebras and we investigate some of their properties. We study the relationship between fuzzy Hom-Lie subalgebras (resp. ideals) and Hom-Lie subalgebras (resp. ideals). For a finite number of fuzzy Hom-Lie subalgebras, we construct a new fuzzy hom-Lie subalgebras on their direct sum. Finally, The properties of fuzzy Hom-Lie subalgebras and fuzzy Hom-Lie ideals under morphisms of Hom-Lie algebras are studied.