Amenability of locally compact quantum groups via the long-time behavior of convolution semigroups

2026/08/04 by Ami Viselter
Mathematics · #math.OA #math.FA #math.GR #math.PR #msc:46L67 #msc:46L30 #msc:46L53 #msc:46L57 #msc:47B38 #msc:47D07

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17 pages. Comments are welcome!

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

We establish a simple characterization of amenability of second countable locally compact quantum groups \mathbbG in terms of the long-time behavior of convolution semigroups of states on \mathbbG. We then investigate the deeper problem of combining amenability of \mathbbG with other approximation properties of the dual quantum group \mathbbG. Specifically, we characterize the combination of ("strong") amenability of \mathbbG with either the failure of property (T) or the presence of the Haagerup property for \mathbbG. These results, which appear to be new even in the classical setting of locally compact groups, produce convolution semigroups on \mathbbG whose behavior is controlled both as time goes to zero and as time goes to infinity.

Citations

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