Extraction Algorithm of Hom-Lie Algebras Based on Solvable and Nilpotent Groups

2023/03/26 by Shaqaqha, Shadi, Kdaisat, Nadeen
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2303.14826

Abstract

Hom-Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom-Lie algebras studied further. In the theory of groups, investigations of the properties of the solvable and nilpotent groups are well-developed. We establish a theory of the solvable and nilpotent Hom-Lie algebras analogous to that of the solvable and nilpotent groups. We also provide examples to illustrate our results and discuss possible directions for further research.

Related

• Universal Algebra of a Hom-Lie Algebra and group-like elements
• On (n+1)-Hom-Lie Algebras Induced by n-Hom-Lie Algebras
• On Hom-algebra structures
• Hom-Lie groups of a class of Hom-Lie algebra
• Classification problem of simple Hom-Lie algebras