The planar algebra of a fixed point subfactor
Annales mathématiques Blaise Pascal, Volume 25 (2018) no. 2, pp. 247-264.

We consider inclusions of type (PA) G (PB) 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 AB. 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(AB) G , with G acting in some natural sense on the bipartite graph algebra P(AB).

On considère des inclusions du type (PA) G (PB) 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 AB. 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(AB) G , avec G agissant dans un certain sens naturel sur l’algèbre de graphe bipartite P(AB).

Published online:
DOI: 10.5802/ambp.376
Classification: 46L65, 46L37
Keywords: Compact quantum group, Fixed point subfactor
Keywords: Groupe quantique compact, Sous-facteur de points fixes
Teodor Banica 1

1 Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Teodor Banica. The planar algebra of a fixed point subfactor. Annales mathématiques Blaise Pascal, Volume 25 (2018) no. 2, pp. 247-264. doi : 10.5802/ambp.376.

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