English

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

Rings and Algebras 2015-05-18 v1 Mathematical Physics math.MP

Abstract

In this paper we construct ternary qq-Virasoro-Witt algebras which qq-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1,1)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 qq-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 qq-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 qq-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

Keywords

Cite

@article{arxiv.1002.4116,
  title  = {Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras},
  author = {F. Ammar and A. Makhlouf and S. Silvestrov},
  journal= {arXiv preprint arXiv:1002.4116},
  year   = {2015}
}