QUANTUM DOUBLE-TORUS

A symmetry extending the T-2-symmetry of the noncommutative torus T-q( 2) is studied in the category of quantum groups. This extended symmetr y is given by the quantum double-torus DTq2 defined as a compact matri x quantum group consisting of the disjoint union of T-2 and T-q2(2). T he bicross-product structure of the polynomial Hopf algebra A(DTq2) is computed. The Haar measure and the complete list of unitary irreducib le representations of Tq22 are determined explicitly. (C) Academie des Sciences/Elsevier, Paris.