Hom-power associative algebras

2010/07/23 by Donald Yau, Yau, Donald
Mathematics · #17A05 #17A15 #17A20 #17D15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1007.4118

openalex publication_date 2010/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• Hom-Algebras and Hom-Coalgebras

Related

• Right Hom-alternative algebras
• Hom-alternative algebras and Hom-Jordan algebras
• Structure and classification of Hom-associative algebras
• Universal Algebra Applied to Hom-Associative Algebras, and More
• On Hom type algebras