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Generalization of n-ary Nambu algebras and beyond
Universit́e de Haute Alsace, France .
Universit́e de Haute Alsace, France .
Lund University. (Mathematics/Applied Mathematics)ORCID iD: 0000-0003-4554-6528
2009 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 8, Article number 083501- p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

Place, publisher, year, edition, pages
2009. Vol. 50, no 8, Article number 083501- p.
Keyword [en]
hom-Nambu algebra, n-ary hom-algebra structure, Hom-Lie algebra
National Category
Algebra and Logic Other Physics Topics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-22078DOI: 10.1063/1.3167801ISI: 000269885700023Scopus ID: 2-s2.0-69749097359OAI: oai:DiVA.org:mdh-22078DiVA: diva2:682600
Available from: 2013-12-28 Created: 2013-10-23 Last updated: 2014-01-10Bibliographically approved

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Silvestrov, S. D.
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