Journal of Generalized Lie Theory and Applications

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

Yaël Frégier, Aron Gohr, and Sergei Silvestrov

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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.

Article information

Source
J. Gen. Lie Theory Appl., Volume 3, Number 4 (2009), 285-295.

Dates
First available in Project Euclid: 6 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1281106596

Digital Object Identifier
doi:10.4303/jglta/S090402

Mathematical Reviews number (MathSciNet)
MR2602991

Zentralblatt MATH identifier
1237.17005

Subjects
Primary: 17A30: Algebras satisfying other identities 16Y99: None of the above, but in this section 17A01: General theory 17A20: Flexible algebras 17D25: Lie-admissible algebras

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

Citation

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


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