Permanence of approximation properties for discrete quantum groups

Freslon, Amaury

Annales de l'Institut Fourier, Tome 65 (2015) no. 4, pp. 1437-1467.

Nous prouvons plusieurs résultats concernant la permanence de la moyennabilité faible et de la propriété de Haagerup pour les groupes quantiques discrets. En particulier, nous améliorons des résultats connus sur les produits libres en autorisant l’amalgamation sur un sous-groupe quantique fini. Nous définissons également une notion de moyennabilité relative pour les groupes quantiques discrets et nous la relions à l’équivalence moyennable d’algèbres de von Neumann, ce qui donne de nouvelles propriétés de permanence.

We prove several results on the permanence of weak amenability and the Haagerup property for discrete quantum groups. In particular, we improve known facts on free products by allowing amalgamation over a finite quantum subgroup. We also define a notion of relative amenability for discrete quantum groups and link it with amenable equivalence of von Neumann algebras, giving additional permanence properties.

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