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Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras

Arnlind, Joakim; Makhlouf, Abdenacer and Silvestrov, Sergei LU (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)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
51
issue
4
publisher
American Institute of Physics
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
2010-06-22 09:30:03
date last changed
2018-05-29 11:52:53
@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},
  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},
  volume       = {51},
  year         = {2010},
}