The exterior product and homology of Hom-Lie algebras
Negur Shahni Karamzadeh, Seyedeh Narges Hosseini, Ali Reza Salemkar
TL;DR
This paper explores the exterior product of Hom-Lie algebras to establish a Hopf formula, construct homology sequences, and analyze capability properties, advancing the algebraic understanding of Hom-Lie structures.
Contribution
It introduces the use of exterior products to derive a Hopf formula and homology sequences for Hom-Lie algebras, which is a novel approach in this area.
Findings
Established the Hopf formula for Hom-Lie algebras
Constructed an eight-term homology sequence
Analyzed capability properties of Hom-Lie algebras
Abstract
In this article, we use the theory of (non-abelian) exterior product of Hom-Lie algebras to prove the Hopf formula for these algebras. As an application, we construct an eight-term sequence in the homology of Hom-Lie algebras. We also investigate the capability property of Hom-Lie algebras via the exterior product.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research