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

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).

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).

Publié le : 2018-11-28
DOI : https://doi.org/10.5802/ambp.376
Classification : 46L65,  46L37
Mots clés: Groupe quantique compact, Sous-facteur de points fixes
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     author = {Teodor Banica},
     title = {The planar algebra of a fixed point subfactor},
     journal = {Annales Math\'ematiques Blaise Pascal},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {25},
     number = {2},
     year = {2018},
     pages = {247-264},
     doi = {10.5802/ambp.376},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2018__25_2_247_0/}
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Banica, Teodor. 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/item/AMBP_2018__25_2_247_0/

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