Title 
Generalization of nary Nambu algebras and beyond 
Authors 
H. Ataguema,
A. Makhlouf,
Sergei Silvestrov

Alternative Location 
http://dx.doi.org/10.1063/1..., Restricted Access 
Publication 
Journal of Mathematical Physics 
Year 
2009 
Volume 
50 
Issue 
8 
Document type 
Article 
Status 
Published 
Quality controlled 
Yes 
Language 
eng 
Publisher 
American Institute of Physics 
Abstract English 
The aim of this paper is to introduce nary Homalgebra structures generalizing the nary algebras of Lie type including nary Nambu algebras, nary NambuLie algebras and nary Lie algebras, and nary algebras of associative type including nary totally associative and nary 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 nary Homalgebra structure starting from an nary algebra and an nary 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 threedimensional HomNambuLie structures with diagonal homomorphism. (C) 2009 American Institute of Physics. DOI: 10.1063/1.3167801 
ISBN/ISSN/Other 
ISSN: 00222488 