Amenable discrete quantum groups
By Reiji Tomatsu. 2003
107 citations recorded by the source corpus.
Z.-J. Ruan has shown that several amenability conditions are all equivalent in the case of discrete Kac algebras. In this paper we extend this work to the case of discrete quantum groups with a quite different method. That is, we show that a discrete quantum group, where we do not assume its unimodularity, has an invariant mean if and only if it satisfies a certain condition, which is called strong Voiculescu amenability in the case of Kac algebras.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0383ff97f18fff87872d97e7cd8df92cba36a963
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Kazhdan's Property T for Discrete Quantum Groups (2008, background): “Wang [18] and studied in detail by Banica [1], [2]. Some discrete group-like properties and proofs have been generalized to (the dual of) compact quantum groups. See, for example, the work of Tomatsu [14] on amenability, the work of Banica and Vergnioux [3] on growth and the work of Vergnioux and Va”
- A Characterization of Right Coideals of Quotient Type and its Application to Classification of Poisson Boundaries (2006, unknown): “= ω(1)forany ω∈ B(K)∗. Hence (id⊗Sˆ)(Vπ) = V∗ π . 2.3. Amenability. We recall the notion of amenability of a discrete quantum group. For a detail of the theory, readers are referred to [2], [3], [4], [22] and references therein. A discrete quantum group (M,∆) is said to be amenable if there exists a”
- The Haagerup property for locally compact quantum groups (2013, background): “2 and the fact that amenability of G implies the coamenability of O G, shown in [70].”