Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2345079
- author
- Arnlind, Joakim ; Makhlouf, Abdenacer and Silvestrov, Sergei LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 52
- issue
- 12
- article number
- 123502
- publisher
- American Institute of Physics (AIP)
- 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
- 2016-04-01 13:59:35
- date last changed
- 2022-04-22 00:49:28
@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]}}, author = {{Arnlind, Joakim and Makhlouf, Abdenacer and Silvestrov, Sergei}}, issn = {{0022-2488}}, language = {{eng}}, number = {{12}}, publisher = {{American Institute of Physics (AIP)}}, 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}}, doi = {{10.1063/1.3653197}}, volume = {{52}}, year = {{2011}}, }