2017/09/23 by Michael Brannan, Brannan, Michael, Sang-Gyun Youn +1
Mathematics · #20G42 #22D12 #22D15 #46L07 #46L89 #81R50 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:20G42 #msc:22D12 #msc:22D15 #msc:46L07 #msc:46L89 #msc:81R50
paper · pdf · doi:10.48550/arxiv.1709.08032
19pages, The proof of Proposition 4.2 in v1 contains a gap, which invalidates the claim in Corollary 4.3 that Fourier algebras of unimodular groups have the completely bounded similarity property. These incorrect results are removed from the current version, v2
arxiv created 2017/11/14 · arxiv updated 2017/11/15
A well-known theorem of Day and Dixmier states that any uniformly bounded representation of an amenable locally compact group G on a Hilbert space is similar to a unitary representation. Within the category of locally compact quantum groups, the conjectural analogue of the Day-Dixmier theorem is that every completely bounded Hilbert space representation of the convolution algebra of an amenable locally compact quantum group should be similar to a ∗-representation. We prove that this conjecture is false for a large class of non-Kac type compact quantum groups, including all q-deformations of compact simply connected semisimple Lie groups. On the other hand, within the Kac framework, we prove that the Day-Dixmier theorem does indeed hold for several new classes of examples, including amenable discrete quantum groups of Kac-type.