Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
F. Ammar, A. Makhlouf, S. Silvestrov

TL;DR
This paper introduces a new family of ternary q-Virasoro-Witt algebras that generalize previous structures, demonstrating their Hom-Nambu-Lie properties across various parameter values using algebraic deformation techniques.
Contribution
It constructs ternary q-Virasoro-Witt algebras as Hom-Nambu-Lie algebras for all parameters, extending prior work on ternary Virasoro-Witt algebras.
Findings
The constructed algebras are Hom-Nambu-Lie for all parameter values.
The q-deformation generalizes previous ternary Virasoro-Witt algebras.
Different construction methods show the universal Hom-Nambu-Lie structure.
Abstract
In this paper we construct ternary -Virasoro-Witt algebras which -deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using 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 -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 -Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of…
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