haagerup_property
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| ==== Stability results ==== | ==== Stability results ==== | ||
| + | * If $\Gamma$ has the Haagerup property, then any quantum subgroup of $\Gamma$ has the Haagerup property. [(ref:DFSW13)] | ||
| + | * 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 $\hat G\tilstar\Z$ has Haagerup property [(ref:Bra11)] | ||
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| * Any finite quantum group | * Any finite quantum group | ||
| + | * Coxeter groups | ||
| * $\mathbb{F}_n$ [(ref:Haa78)], $\mathrm{SL}_2(\Z)$ | * $\mathbb{F}_n$ [(ref:Haa78)], $\mathrm{SL}_2(\Z)$ | ||
| * $\hat O_N^+$, $\hat U_N^+$ [(ref:Bra11)] | * $\hat O_N^+$, $\hat U_N^+$ [(ref:Bra11)] | ||
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| doi : 10.1007/s00220-014-2052-7 | doi : 10.1007/s00220-014-2052-7 | ||
| url : https://doi.org/10.1007/s00220-014-2052-7 | url : https://doi.org/10.1007/s00220-014-2052-7 | ||
| + | )] | ||
| + | |||
| + | |||
| + | [(ref:FMP17>> | ||
| + | title : On compact bicrossed products | ||
| + | journal : Journal of Noncommutative Geometry | ||
| + | volume : 11 | ||
| + | number : 4 | ||
| + | pages : 1521--1591 | ||
| + | year : 2017 | ||
| + | doi : 10.4171/JNCG/11-4-10 | ||
| + | url : http://dx.doi.org/10.4171/JNCG/11-4-10 | ||
| + | author : Pierre Fima, Kunal Mukherjee and Issan Patri | ||
| )] | )] | ||
| ~~REFNOTES ref ~~ | ~~REFNOTES ref ~~ | ||
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