Noncommutative index theory for mirror quantum spheres

Piotr M. Hajac; Rainer Matthes; Wojciech Szymański

doi:10.1016/j.crma.2006.09.021

Functional Analysis

Noncommutative index theory for mirror quantum spheres
[Théorie de l'indice non commutative pour des sphères quantiques miroirs]

Présenté par : Alain Connes

Piotr M. Hajac ^1,² ; Rainer Matthes ² ; Wojciech Szymański ³

¹ Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
² Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, ul. Hoża 74, Warszawa, 00-682 Poland
³ School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia

Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 731-736.

Résumé
Abstract

Nous introduisons et analysons un nouveau type de 2-sphères quantiques. Nous appliquons la théorie de l'indice pour les fibrés en droites non commutatifs sur ces sphères afin de déduire que les espaces lenticulaires quantiques sont des exemples d'extensions principales de $C^{*}$ -algèbres qui ne sont pas des produits croisés.

We introduce and analyse a new type of quantum 2-spheres. Then we apply index theory for noncommutative line bundles over these spheres to conclude that quantum lens spaces are non-crossed-product examples of principal extensions of $C^{*}$ -algebras.

Reçu le : 2005-12-03
Accepté le : 2006-09-26
Publié le : 2006-11-28

DOI : 10.1016/j.crma.2006.09.021

Affiliations des auteurs :

Piotr M. Hajac ^{1, 2} ; Rainer Matthes ² ; Wojciech Szymański ³

¹ Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
² Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, ul. Hoża 74, Warszawa, 00-682 Poland
³ School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia

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     title = {Noncommutative index theory for mirror quantum spheres},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {731--736},
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     volume = {343},
     number = {11-12},
     year = {2006},
     doi = {10.1016/j.crma.2006.09.021},
     language = {en},
}

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Piotr M. Hajac; Rainer Matthes; Wojciech Szymański. Noncommutative index theory for mirror quantum spheres. Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 731-736. doi : 10.1016/j.crma.2006.09.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.021/

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