Quantum Double-Torus

Details Quantum Double-Torus Quantum Double-Torus

1998-03-20

arxiv.org/abs/math/9803092v2

Mathematics

Quantum Algebra

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

Scientific paper

10.1016/S0764-4442(98)89162-3

A symmetry extending the $T^2$-symmetry of the noncommutative torus $T^2_q$ 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 $T^2_{q^2}$. 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.

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