The C*-algebra obtained by completing the quantum group Funq (SU(2))

Abstract

For positive q, the scalar product defined by the integral on Funq(SU(2)) is used to complete Funq(SU(2)) to a Hilbert space ℋq. The dual map to the coproduct on Funq(SU(2)) makes ℋq into a Banach algebra without unit. Multiplication from the left defines a *-representation of Funq(SU(2)) on ℋq and thus Funq(SU(2)) can be completed to a C*-algebra ℱq. This C*-algebra is shown to coincide with the C*-algebra SUν(2) considered by Woronowicz [Publ. RIMS, Kyoto Univ. 23, 117 (1987)]. General representations of ℱq are discussed and the spectrum of ℱq and its Jacobson topology are calculated.