The planar algebra of a fixed point subfactor

Teodor Banica

doi:10.5802/ambp.376

Teodor Banica ¹

¹ Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise, France

Annales mathématiques Blaise Pascal, Tome 25 (2018) no. 2, pp. 247-264.

Résumé
Abstract

On considère des inclusions du type ${(P \otimes A)}^{G} \subset {(P \otimes B)}^{G}$ , où $G$ est un groupe quantique compact de type Kac agissant sur un facteur de type ${II}_{1}$ $P$ , et sur une inclusion de Markov de $C^{*}$ -algèbres de dimension finie $A \subset B$ . Dans le cas $[A, B] = 0$ , qui couvre essentiellement tous les exemples connus, on montre que l’algèbre planaire d’un tel sous-facteur est de la forme $P {(A \subset B)}^{G}$ , avec $G$ agissant dans un certain sens naturel sur l’algèbre de graphe bipartite $P (A \subset B)$ .

We consider inclusions of type ${(P \otimes A)}^{G} \subset {(P \otimes B)}^{G}$ , where $G$ is a compact quantum group of Kac type acting on a ${II}_{1}$ factor $P$ , and on a Markov inclusion of finite dimensional $C^{*}$ -algebras $A \subset B$ . In the case $[A, B] = 0$ , which basically covers all known examples, we show that the planar algebra of such a subfactor is of the form $P {(A \subset B)}^{G}$ , with $G$ acting in some natural sense on the bipartite graph algebra $P (A \subset B)$ .

Publié le : 2018-11-27

DOI : 10.5802/ambp.376

Classification : 46L65, 46L37
Keywords: Compact quantum group, Fixed point subfactor
Mots clés : Groupe quantique compact, Sous-facteur de points fixes

Affiliations des auteurs :

Teodor Banica ¹

¹ Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Teodor Banica. The planar algebra of a fixed point subfactor. Annales mathématiques Blaise Pascal, Tome 25 (2018) no. 2, pp. 247-264. doi : 10.5802/ambp.376. https://ambp.centre-mersenne.org/articles/10.5802/ambp.376/

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