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Generalization of n-ary Nambu algebras and beyond

Ataguema, H.; Makhlouf, A. and Silvestrov, Sergei LU (2009) In Journal of Mathematical Physics 50(8).
Abstract
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... (More)
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] (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
50
issue
8
publisher
American Institute of Physics
external identifiers
  • wos:000269885700023
  • scopus:69749097359
ISSN
0022-2488
DOI
10.1063/1.3167801
language
English
LU publication?
yes
id
e5c9af90-0abe-4b5c-8034-ed8fb3727479 (old id 1490682)
date added to LUP
2009-10-19 14:49:53
date last changed
2017-12-10 04:22:26
@article{e5c9af90-0abe-4b5c-8034-ed8fb3727479,
  abstract     = {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]},
  author       = {Ataguema, H. and Makhlouf, A. and Silvestrov, Sergei},
  issn         = {0022-2488},
  language     = {eng},
  number       = {8},
  publisher    = {American Institute of Physics},
  series       = {Journal of Mathematical Physics},
  title        = {Generalization of n-ary Nambu algebras and beyond},
  url          = {http://dx.doi.org/10.1063/1.3167801},
  volume       = {50},
  year         = {2009},
}