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kirchberg_property

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Kirchberg factorization property

Definition

Let $G$ be a compact quantum group. The discrete dual $\hat G$ is said to have the Kirchberg factorization property or property (F) if the Haar state $h$ on $C(G)$ is amenable. [BW16]

Results

The following quantum groups have (F)

  • $\hat U_N^+$, $\hat O_N^+$ for $N\neq 3$ [BW16]
  • $\hat S_N$ for any $N$ [BCF18]
  • $\hat H^{s+}_N$ for $N\ge 4$ and $1\le s\le\infty$ [BCF18]
  • Any Abelian discrete quantum group (i.e. dual of a compact group)

Relation with other properties

If $\Gamma=\hat G$ has (F), then

  • $\Gamma$ has the Connes embedding property [BBCW17]

Discrete quantum group $\Gamma=\hat G$ has (F) if

References

[BW16] Angshuman Bhattacharya, Shuzhou Wang, 2016. Kirchberg's factorization property for discrete quantum groups. Bulletin of the London Mathematical Society, 48(5), pp.866–876.
[BCF18] Michael Brannan, Alexandru Chirvasitu, Amaury Freslon, 2018. Topological generation and matrix models for quantum reflection groups.
[BBCW17] Angshuman Bhattacharya, Michael Brannan, Alexandru Chirvasitu, Shuzhou Wang, 2017. Kirchberg factorization and residual finiteness for discrete quantum groups.
kirchberg_property.txt · Last modified: 2021/11/23 11:56 (external edit)

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