Hom-alternative algebras and Hom-Jordan algebras
Abdenacer Makhlouf

TL;DR
This paper introduces Hom-alternative and Hom-Jordan algebras, explores their properties, and provides construction methods from classical algebras, establishing connections between Hom-associative and Hom-Jordan structures.
Contribution
It is the first to define and analyze Hom-alternative and Hom-Jordan algebras, expanding the framework of Hom-algebra theory with new constructions and properties.
Findings
Hom-alternative and Hom-Jordan algebras are well-defined structures.
Construction procedures from classical algebras are established.
Polarization of Hom-associative algebra yields Hom-Jordan algebra.
Abstract
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms
