approximation_properties_summary
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Table of Contents
Summary of results on approximation properties for discrete QGs
More information including citations of original sources is available in the individual articles.
Mutual relationships
Stability results
| Products | Subgroups | Quotients | Dual top. gen. | ||||
|---|---|---|---|---|---|---|---|
| Direct | Free | Wreath | Free wr. | ||||
| Kirchberg (F) | |||||||
| Resid. finite | yes | ||||||
| Kazhdan (T) | yes | ||||||
| Haagerup | yes | ||||||
| Amenable | no | yes | |||||
Concrete examples
free CMQG duals (assuming  high enough) | half-lib. duals | non-unimod. | Abelian | Groups | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
 |  |  |  |  |  |  |  |  | |||
| Kirchberg (F) | yes 1) | yes 1) | yes2) | yes2) | yes | ||||||
| Resid. finite | yes 1) | yes 1) | yes2) | yes2) | yes | no | |||||
| Kazhdan (T) | no | no | no | no | no | no | |||||
| Haagerup | yes | yes | yes | yes | yes | yes | yes | ||||
| Amenable |  | yes | yes | ||||||||
Further reading
- Michael Brannan. Approximation properties for locally compact quantum groups, 2016.
- Nathanial P. Brown and Narutaka Ozawa, C*-algebras and Finite-Dimensional Approximations, American Mathematical Society, 2008.
approximation_properties_summary.1570195483.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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