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Author Ammar, F. ♦ Makhlouf, A. ♦ Silvestrov, S.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-02-22
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword Mathematics - Rings and Algebras ♦ Mathematical Physics ♦ 17B68 ♦ 16S80 ♦ 17B37 ♦ math ♦ physics:math-ph
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.
Educational Use Research
Learning Resource Type Article


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