On n-ary Hom-Nambu and Hom-Maltsev algebras

2010/04/27 by Donald Yau, Yau, Donald
Mathematics · Physics and Astronomy · #17A40 #17A42 #17A75 #17C50 #17D05 #17D10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1004.4795

openalex publication_date 2010/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hom-alternative and Hom-Jordan algebras are shown to give rise to Hom-Nambu algebras of arities 2^k+1 + 1. The class of n-ary Hom-Maltsev algebras is studied. Multiplicative n-ary Hom-Nambu-Lie algebras are shown to be n-ary Hom-Maltsev algebras. Examples of ternary Hom-Maltsev algebras that are not ternary Hom-Nambu-Lie algebras are given. Ternary Hom-Maltsev algebras are shown to arise from composition algebras.

Citations

• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-alternative algebras and Hom-Jordan algebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry

Related

• n-ary Hom-Nambu algebras
• A note on relations between Hom-Malcev algebras and Hom-Lie-Yamaguti algebras
• A Hom-associative analogue of n-ary Hom-Nambu algebras
• Hom-Lie triple system and Hom-Bol algebra structures on Hom-Malcev and right Hom-alternative algebras
• Hopf Structure in Nambu-Lie n-Algebras