Generalization of n-ary Nambu algebras and beyond
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1490682
- author
- Ataguema, H. ; Makhlouf, A. and Silvestrov, Sergei LU
- organization
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 50
- issue
- 8
- publisher
- American Institute of Physics (AIP)
- 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
- 2016-04-01 14:56:49
- date last changed
- 2022-04-14 20:29:53
@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 (AIP)}},
series = {{Journal of Mathematical Physics}},
title = {{Generalization of n-ary Nambu algebras and beyond}},
url = {{http://dx.doi.org/10.1063/1.3167801}},
doi = {{10.1063/1.3167801}},
volume = {{50}},
year = {{2009}},
}