Journal of Generalized Lie Theory and Applications
- J. Gen. Lie Theory Appl.
- Volume 3, Number 4 (2009), 285-295.
Unital algebras of Hom-associative type and surjective or injective twistings
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.
J. Gen. Lie Theory Appl., Volume 3, Number 4 (2009), 285-295.
First available in Project Euclid: 6 August 2010
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Frégier, Yaël; Gohr, Aron; Silvestrov, Sergei. Unital algebras of Hom-associative type and surjective or injective twistings. J. Gen. Lie Theory Appl. 3 (2009), no. 4, 285--295. doi:10.4303/jglta/S090402. https://projecteuclid.org/euclid.jglta/1281106596