residual_finiteness
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residual_finiteness [2019/09/06 13:06] d.gromada |
residual_finiteness [2021/11/23 11:56] (current) |
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| ==== Known examples ==== | ==== Known examples ==== | ||
| - | * $U_N^+$ and $O_N^+$ for $N\neq 3$ [(ref:Chi15)] | + | * $\hat U_N^+$ and $\hat O_N^+$ for $N\neq 3$ [(ref:Chi15)] |
| * $\hat S_N$ for any $N$ [(ref:BCF18)] | * $\hat S_N$ for any $N$ [(ref:BCF18)] | ||
| * $\hat H^{s+}_N$ for $N\ge 4$ and $1\le s\le\infty$ [(ref:BCF18)] | * $\hat H^{s+}_N$ for $N\ge 4$ and $1\le s\le\infty$ [(ref:BCF18)] | ||
| + | * Any Abelian discrete quantum group (i.e. dual of a compact group) | ||
| ==== Known non-examples ==== | ==== Known non-examples ==== | ||
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| If $\Gamma=\hat G$ is residually finite, then | If $\Gamma=\hat G$ is residually finite, then | ||
| - | * $\Gamma$ has property (F) [(ref:BBCW17)] | + | * $\Gamma$ has [[kirchberg_property|property (F)]] [(ref:BBCW17)] |
| * $\Gamma$ has the Connes embedding property [(ref:BBCW17)] | * $\Gamma$ has the Connes embedding property [(ref:BBCW17)] | ||
| - | * $G$ is of Kac type [(ref:Sol05)] | + | * $\Gamma$ is [[unimodularity|unimodular]] [(ref:Sol05)] |
| Quantum group $\Gamma=\hat G$ is residually finite if | Quantum group $\Gamma=\hat G$ is residually finite if | ||
| - | * $\Gamma$ has [[kazhdan_property|property (T)]] and property (F) [(ref:BBCW17)] | + | * $\Gamma$ has [[kazhdan_property|property (T)]] and [[kirchberg_property|property (F)]] [(ref:BBCW17)] |
residual_finiteness.1567775216.txt.gz ยท Last modified: 2021/11/23 11:56 (external edit)
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