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

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.

References in corpus (10)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• Ternary Virasoro - Witt Algebra
• On unitality conditions for Hom-associative algebras
• Quasi-Deformations of sl_2(\F) using twisted derivations
• Hom-Algebras and Hom-Coalgebras
• On hom-algebras with surjective twisting
• Virasoro 3-algebra from scalar densities

Cited by in corpus (14)

• Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
• Representations and Cohomology of n-ary multiplicative Hom-Nambu-Lie algebras
• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• A Hom-associative analogue of n-ary Hom-Nambu algebras
• Hom-algebras via PROPs
• Cohomology of Hom-Leibniz and $n$-ary Hom-Nambu-Lie superalgebras
• Quadratic $n$-ary Hom-Nambu algebras
• Multi-parameter formal deformations of ternary hom-Nambu-Lie algebras
• On q-deformed infinite-dimensional n-algebra
• Equivalent description of Hom-Lie algebroids
• Double derivations of $n-$Hom-Lie color algebras
• Non-Commutative ternary Nambu-Poisson algebras and ternary Hom-Nambu-Poisson algebras