Quantum Double-Torus

Abstract

A symmetry extending the $T^2$-symmetry of the noncommutative torus $T_q^2$ is studied in the category of quantum groups. This extended symmetry is given by the quantum double-torus defined as a compact matrix quantum group consisting of the disjoint union of $T^2$ and $T_{q^2}^2$. The bicross-product structure of the polynomial Hopf algebra of the quantum double-torus is computed. The Haar measure and the complete list of unitary irreducible representations of the quantum double-torus are determined explicitly.

6 pages, no figures, amslatex, reformatted for Comptes Rendus, references added, typos and French corrected

Cited by in corpus (4)

• Quantum Group of Isometries in Classical and Noncommutative Geometry
• Braided Hopf algebras from twisting
• Multiple noncommutative tori and Hopf algebras
• Quantum symmetry groups of noncommutative tori