| Title | Generalization of n-ary 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 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. (C) 2009 American Institute of Physics. DOI: 10.1063/1.3167801 |
| ISBN/ISSN/Other | ISSN: 0022-2488 |
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