A Hom-associative analogue of n-ary Hom-Nambu algebras

2010/05/13 by Yau, Donald
#17A40 #17A42 #17B81 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1005.2373

Abstract

It is shown that every n-ary totally Hom-associative algebra with equal twisting maps yields an n-ary Hom-Nambu algebra via an n-ary version of the commutator bracket. The class of n-ary totally Hom-associative algebras is shown to be closed under twisting by self-weak morphisms. Every multiplicative n-ary totally Hom-associative algebra yields a sequence of multiplicative totally Hom-associative algebras of exponentially higher arities. Under suitable conditions, an n-ary totally Hom-associative algebra gives an (n-k)-ary totally Hom-associative algebra.

Related

• n-ary Hom-Nambu algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• On Hom type algebras
• On hom-algebras with surjective twisting
• Hom-power associative algebras