# REPRESENTATION AND DUALITY OF UNIMODULAR C*-DISCRETE QUANTUM GROUPS

• Lining, Jiang
• Published : 2008.03.31
• 55 3

#### Abstract

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

#### Keywords

discrete quantum group$C^*$-algebra;representation;duality

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#### Cited by

1. On projective representations for compact quantum groups vol.260, pp.12, 2011, https://doi.org/10.1016/j.jfa.2011.02.022
2. C*-Homomorphisms and duality of C*-discrete quantum groups vol.50, pp.2, 2009, https://doi.org/10.1007/s11202-009-0041-4