REPRESENTATION AND DUALITY OF UNIMODULAR C*-DISCRETE QUANTUM GROUPS

Title & Authors
REPRESENTATION AND DUALITY OF UNIMODULAR C*-DISCRETE QUANTUM GROUPS
Lining, Jiang;

Abstract
Suppose that D is a $\small{C^*}$-discrete quantum group and $\small{D_0}$ 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 $\small{C^*}$-representation $\small{\theta}$ 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 $\small{\theta}$(D) in L(H).
Keywords
discrete quantum group$\small{C^*}$-algebra;representation;duality;
Language
English
Cited by
1.
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2.
C*-Homomorphisms and duality of C*-discrete quantum groups, Siberian Mathematical Journal, 2009, 50, 2, 360
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