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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

Arnlind, Joakim; Makhlouf, Abdenacer and Silvestrov, Sergei LU (2011) In Journal of Mathematical Physics 52(12).
Abstract
As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary... (More)
As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197] (Less)
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organization
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type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
52
issue
12
publisher
American Institute of Physics
external identifiers
  • wos:000298641000020
  • scopus:84855279256
ISSN
0022-2488
DOI
10.1063/1.3653197
language
English
LU publication?
yes
id
4518bdf4-97f4-487a-af96-7bb1a4520be6 (old id 2345079)
date added to LUP
2012-02-24 13:16:26
date last changed
2017-11-12 03:42:05
@article{4518bdf4-97f4-487a-af96-7bb1a4520be6,
  abstract     = {As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]},
  articleno    = {123502},
  author       = {Arnlind, Joakim and Makhlouf, Abdenacer and Silvestrov, Sergei},
  issn         = {0022-2488},
  language     = {eng},
  number       = {12},
  publisher    = {American Institute of Physics},
  series       = {Journal of Mathematical Physics},
  title        = {Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras},
  url          = {http://dx.doi.org/10.1063/1.3653197},
  volume       = {52},
  year         = {2011},
}