Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
(2010) In Journal of Mathematical Physics 51(4).- Abstract
- The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction. (C) 2010 American Institute of Physics.... (More)
- The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction. (C) 2010 American Institute of Physics. [doi:10.1063/1.3359004] (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1619390
- author
- Arnlind, Joakim ; Makhlouf, Abdenacer and Silvestrov, Sergei LU
- organization
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 51
- issue
- 4
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- wos:000277242500038
- scopus:77953252041
- ISSN
- 0022-2488
- DOI
- 10.1063/1.3359004
- project
- Non-commutative Geometry in Mathematics and Physics
- language
- English
- LU publication?
- yes
- id
- a5c13da8-9768-4b61-9bbc-cb1fdd7e4330 (old id 1619390)
- date added to LUP
- 2016-04-01 14:33:16
- date last changed
- 2022-02-04 21:31:54
@article{a5c13da8-9768-4b61-9bbc-cb1fdd7e4330,
abstract = {{The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction. (C) 2010 American Institute of Physics. [doi:10.1063/1.3359004]}},
author = {{Arnlind, Joakim and Makhlouf, Abdenacer and Silvestrov, Sergei}},
issn = {{0022-2488}},
language = {{eng}},
number = {{4}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Journal of Mathematical Physics}},
title = {{Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras}},
url = {{http://dx.doi.org/10.1063/1.3359004}},
doi = {{10.1063/1.3359004}},
volume = {{51}},
year = {{2010}},
}