Liberation theory for noncommutative homogeneous spaces

[Théorie de liberation pour les espaces homogènes non commutatifs]

Banica, Teodor¹

¹ Département des Mathématiques, Cergy-Pontoise University, 95000 Cergy-Pontoise, France

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 26 (2017) no. 1, pp. 127-156.

Abstract (VO)

We discuss the liberation question, in the homogeneous space setting. Our first series of results concerns the axiomatization and classification of the families of compact quantum groups $G=\left(G_N\right)$ which are “uniform”, in a suitable sense. We study then the quotient spaces of type $X=(G_M\times G_N)/(G_L\times G_{M-L}\times G_{N-L})$, and the liberation operation for them, with a number of algebraic and probabilistic results.

Résumé

On étudie le problème de liberation, dans le cadre des espaces homogènes. Notre première série de résultats concerne l’axiomatisation et la classification des familles de groupes quantiques compacts $G=\left(G_N\right)$ qui sont « uniformes », dans un sens convenable. On étudie ensuite les espaces quotient du type $X=(G_M\times G_N)/(G_L\times G_{M-L}\times G_{N-L})$, et l’opération de liberation pour ces espaces, avec des résultats de nature algébrique et probabiliste.

Détail

Reçu le : 2015-12-14
Accepté le : 2016-03-07
Publié le : 2017-02-07

DOI : 10.5802/afst.1527

Classification : 46L65, 46L54
Mots-clés : Liberation theory, Homogeneous space

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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