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Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

Ammar, F.; Makhlouf, A. and Silvestrov, Sergei LU (2010) In Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00 43(26).
Abstract
In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie... (More)
In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00
volume
43
issue
26
publisher
IOP Publishing
external identifiers
  • wos:000278544000009
  • scopus:77953344685
ISSN
1751-8113
DOI
10.1088/1751-8113/43/26/265204
language
English
LU publication?
yes
id
1d20f24f-6348-491f-8ea6-b205c0e49fb0 (old id 1630987)
date added to LUP
2010-07-22 13:21:41
date last changed
2018-05-29 09:26:25
@article{1d20f24f-6348-491f-8ea6-b205c0e49fb0,
  abstract     = {In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters.},
  author       = {Ammar, F. and Makhlouf, A. and Silvestrov, Sergei},
  issn         = {1751-8113},
  language     = {eng},
  number       = {26},
  publisher    = {IOP Publishing},
  series       = {Journal of Physics A: Mathematical and Theoretical2007-01-01+01:00},
  title        = {Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras},
  url          = {http://dx.doi.org/10.1088/1751-8113/43/26/265204},
  volume       = {43},
  year         = {2010},
}