L^2-Betti numbers of coamenable quantum groups - Mathematics Operator AlgebrasReport as inadecuate




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Abstract: We prove that a compact quantum group is coamenable if and only if itscorepresentation ring is amenable. We further propose a Foelner condition forcompact quantum groups and prove it to be equivalent to coamenability. Usingthis Foelner condition, we prove that for a coamenable compact quantum groupwith tracial Haar state, the enveloping von Neumann algebra is dimension flatover the Hopf algebra of matrix coefficients. This generalizes a theorem ofLueck from the group case to the quantum group case, and provides examples ofcompact quantum groups with vanishing L^2-Betti numbers.



Author: David Kyed

Source: https://arxiv.org/







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