A cohomological description of property (T) for quantum groups

2010/03/26 by David Kyed, Kyed, David
Mathematics · #16T05 #46L52 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:16T05 #msc:46L52

paper · pdf · doi:10.48550/arxiv.1003.5181

v2: Title changed, 27 pages, to appear in J. Funct. Anal

arxiv created 2011/05/17 · arxiv updated 2011/05/18

Abstract

We prove a Delorme-Guichardet type theorem for discrete quantum groups expressing property (T) of the quantum group in question in terms of its first cohomology groups. As an application, we show that the first L²-Betti number of a discrete property (T) quantum group vanishes.

Related

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• Kazhdan's Property T for Discrete Quantum Groups
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• Permanence of approximation properties for discrete quantum groups
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