Hom-power associative algebras

Abstract

A generalization of power associative algebra, called Hom-power associative algebra, is studied. The main result says that a multiplicative Hom-algebra is Hom-power associative if and only if it satisfies two identities of degrees three and four. It generalizes Albert's result that power associativity is equivalent to third and fourth power associativity. In particular, multiplicative right Hom-alternative algebras and non-commutative Hom-Jordan algebras are Hom-power associative.

24 pages

References in corpus (11)

• Deformations of Lie Algebras using $\sigma$-derivations
• Hom-algebras and homology
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Hom-quantum groups III: Representations and module Hom-algebras
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• Hom-Algebras and Hom-Coalgebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
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Cited by in corpus (5)

• Non-commutative Hom-Poisson algebras
• Some characterizations of Hom-Leibniz algebras
• A twisted generalization of Novikov-Poisson algebras
• Right Hom-alternative algebras
• The Mikheev identity in right Hom-alternative algebras