HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS

Year 2010, Volume: 8 Issue: 8, 177 - 190, 01.12.2010

Abdenacer Makhlouf

Abstract

The main feature of Hom-algebras is that the identities defining the structures are twisted by homomorphisms. 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 plus algebra of Hom-associative algebra leads to Hom-Jordan algebra.

Keywords

alternative algebra, Hom-alternative algebra, Jordan algebra, Hom-Jordan algebra

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• Universit´e de Haute-Alsace Laboratoire de Math´ematiques Informatique et Applications bis rue des Fr`eres Lumi`ere Mulhouse, France e-mail: [e-mail]