haagerup_property
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haagerup_property [2021/11/23 11:56] (current) |
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| * Let $G$ be a CQG, $H\subset G$ a finite index subgroup (i.e. $C(G/H):=\{a\in C_{\rm u}(G)\mid (\id\otimes p)\Delta(a)=a\otimes 1\}$, where $p$ is the surjection $C_{\rm u}(G)\to C_{\rm u}(H)$, is finite dimensional). If $\hat H$ has the Haagerup property, then $\hat G$ has the Haagerup property. [(ref:FMP17)] | * Let $G$ be a CQG, $H\subset G$ a finite index subgroup (i.e. $C(G/H):=\{a\in C_{\rm u}(G)\mid (\id\otimes p)\Delta(a)=a\otimes 1\}$, where $p$ is the surjection $C_{\rm u}(G)\to C_{\rm u}(H)$, is finite dimensional). If $\hat H$ has the Haagerup property, then $\hat G$ has the Haagerup property. [(ref:FMP17)] | ||
| * Free product $\Gamma_1*\Gamma_2$ has the Haagerup property if and only if both $\Gamma_1$ and $\Gamma_2$ have the Haagerup property [(ref:DFSW13)] | * Free product $\Gamma_1*\Gamma_2$ has the Haagerup property if and only if both $\Gamma_1$ and $\Gamma_2$ have the Haagerup property [(ref:DFSW13)] | ||
| - | * If $\Gamma$ [[unimodularity|unimodular]] has Haagerup property, then also $\Gamma\tilstar\Z$ has Haagerup property [(ref:Bra11)] | ||
haagerup_property.1570612551.txt.gz ยท Last modified: 2021/11/23 11:56 (external edit)
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