alexa Unital algebras of Hom-associative type and surjective
ISSN: 1736-4337

Journal of Generalized Lie Theory and Applications
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Research Article

Unital algebras of Hom-associative type and surjective or injective twistings

Yael FREGIER1*, Aron GOHR 1, and Sergei SILVESTROV 2

1Mathematics Research Unit, University of Luxembourg, 162A Avenue de la faiencerie, L-1511 Luxembourg, Grand-Duchy of Luxembourg

2Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden

E-mails: [email protected], [email protected], [email protected]

Received date: August 25, 2009, Revised date: October 29, 2009

 

Abstract

In this paper, we introduce a common generalizing framework for alternative types of Hom-associative algebras. We show that the observation that unital Hom-associative algebras with surjective or injective twisting map are already associative has a generalization in this new framework. We also show by construction of a counterexample that another such generalization fails even in a very restricted particular case. Finally, we discuss an application of these observations by answering in the negative the question whether nonassociative algebras with unit such as the octonions may be twisted by the composition trick into Hom-associative algebras.

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