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 (6)

• Hom-algebras and homology
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Hom-Algebras and Hom-Coalgebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• A Hom-associative analogue of n-ary Hom-Nambu algebras

Cited by in corpus (4)

• Non-commutative Hom-Poisson algebras
• Some characterizations of Hom-Leibniz algebras
• A twisted generalization of Novikov-Poisson algebras
• Right Hom-alternative algebras