De Finetti theorems for a Boolean analogue of easy quantum groups
arXiv:1507.05563
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. [Modified]Definition of the Boolean quantum semigroups on categories of interval partitions [Delete]Classification of categories of interval partitions [Add]Proof of the positiveness of the Haar functionals (in particular they are Haar states)
26 pages
References in corpus (5)
- A noncommutative de Finetti theorem: Invariance under quantum permutations is equivalent to freeness with amalgamation
- Cumulants in noncommutative probability II. Generalized Gaussian random variables
- A noncommutative De Finetti theorem for boolean independence
- Extended de Finetti theorems for boolean independence and monotone independence
- General de Finetti type theorems in noncommutative probability