Open Access
December 2009 Unital algebras of Hom-associative type and surjective or injective twistings
Yaël Frégier, Aron Gohr, Sergei Silvestrov
J. Gen. Lie Theory Appl. 3(4): 285-295 (December 2009). DOI: 10.4303/jglta/S090402


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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Yaël Frégier. Aron Gohr. Sergei Silvestrov. "Unital algebras of Hom-associative type and surjective or injective twistings." J. Gen. Lie Theory Appl. 3 (4) 285 - 295, December 2009.


Published: December 2009
First available in Project Euclid: 6 August 2010

zbMATH: 1237.17005
MathSciNet: MR2602991
Digital Object Identifier: 10.4303/jglta/S090402

Primary: 16Y99 , 17A01 , 17A20 , 17A30 , 17D25

Keywords: Associative rings and algebras , Flexible algebras , Lie-admissible algebras , Nonassociative algebras , Nonassociative rings

Rights: Copyright © 2009 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • No. 4 • December 2009
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