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 | |||||||
| Kazhdan (T) | |||||||
| Haagerup | |||||||
| Amenable | |||||||
Concrete examples
free CMQG duals (assuming  high enough) |
|||||
|---|---|---|---|---|---|
 |  |  |  |  |
|
| Kirchberg (F) | yes 1) | yes 1) | yes2) | yes2) | yes |
| Resid. finite | yes 1) | yes 1) | yes2) | yes2) | yes |
| Kazhdan (T) | no | no | no | no | no |
| Haagerup | yes | yes | yes | yes | yes |
| Amenable |  | ||||
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.1570183768.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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