The Property of Rapid Decay for Discrete Quantum Groups

By Roland Vergnioux. 2020

65 citations recorded by the source corpus.

We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We then investigate examples, proving in particular the Property of Rapid Decay for unimodular free quantum groups. We finally check that the applications to the K-theory of the reduced group C*-algebras carry over to the quantum case.

View Paper: https://www.semanticscholar.org/paper/46d959390047bfe86d9a2cc83a0daa685a208c39

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Michael Brannan
2. Amaury Freslon
3. K. De Commer
4. Matthew Daws
5. Yusuke Isono

Citations in the corpus

• Reduced operator algebras of trace-preserving quantum automorphism groups (2012, background): “The main difference between the present situation and the one in [33] is that for quantum automorphism groups, the fusion rules U ⊠ U ∼= ⊕2min{n,k} r=0 U k+n−r imply that each tensor product U ⊠ U contains both even and odd length subrepresentations, whereas in the orthogonal case all subrepresentat”
• Approximation properties for free orthogonal and free unitary quantum groups (2011, methodology): “Combining our proof of the HAP for L∞(O+N ) and L ∞(U+N ) with a version of the Haagerup inequality for these quantum groups proved by Vergnioux [35], we are also able to show that the reduced C∗-algebras C(O+N ) and C(U + N ) have the metric approximation property.”