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arXiv · 1002.4116

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

F. Ammar·A. Makhlouf·S. Silvestrov
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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 article 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 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 ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

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BibTeXRIS

F. Ammar, A. Makhlouf, S. Silvestrov. 2010-02-22. Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras. https://doi.org/10.1088/1751-8113%2F43%2F26%2F265204

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