Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
(2010) In Journal of Physics A: Mathematical and Theoretical 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1630987
- author
- Ammar, F. ; Makhlouf, A. and Silvestrov, Sergei LU
- organization
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Physics A: Mathematical and Theoretical
- 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
- 2016-04-01 13:08:47
- date last changed
- 2022-02-26 19:34:13
@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 Theoretical}},
title = {{Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras}},
url = {{http://dx.doi.org/10.1088/1751-8113/43/26/265204}},
doi = {{10.1088/1751-8113/43/26/265204}},
volume = {{43}},
year = {{2010}},
}