De Finetti Theorem for a Boolean Analogue of Easy Quantum Groups
Vol. 24 (2017), No. 3, Page 355-398.
Hayase, Tomohiro
De Finetti Theorem for a Boolean Analogue of Easy Quantum Groups
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
We show an organized form of quantum de Finetti theorem for Boolean independence. We define a Boolean analogue of easy quantum groups for the categories of interval partitions, which is a family of sequences of quantum semigroups. We construct the Haar states on those quantum semigroups. The proof of our de Finetti theorem is based on the analysis of the Haar states.
Keywords: Free probability, easy quantum groups, de Finetti, quantum invariance, Boolean independence, Bernoulli law
Mathematics Subject Classification (2010): Primary 46L54; 46L53, 46L65, 05E10, 16T30, 20G42, 60G09
Mathematical Reviews Number: MR3700487
Received: 2016-11-04
