Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
Ammar, F.; Makhlouf, A.; Silvestrov, Sergei (2010). Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras. Journal of Physics A: Mathematical and Theoretical, 43, (26)
|
Published
|
English
Authors:
Ammar, F.
;
Makhlouf, A.
;
Silvestrov, Sergei
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Research Group:
Non-commutative Geometry-lup-obsolete
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.
Cite this