Quantization and Morita equivalence for constant Dirac structures on tori

[Quantification et équivalence de Morita des structures de Dirac constantes sur les tores]

Tang, Xiang ; Weinstein, Alan

Annales de l'Institut Fourier, Tome 54 (2004), p. 1565-1580 / Harvested from Numdam

Résumé

Nous définissons une quantification $C^*$-algebrique des structures de Dirac constantes sur les tores, et nous démontrons que l’équivalence à $O(n,n|\mathbb {Z})$ près des structures implique l’équivalence de Morita de leurs quantifications. Ce résultat complète et généralise un théorème de Rieffel et Schwarz, donné dans le cadre des structures de Poisson.

Abstract

We define a $C^*$-algebraic quantization of constant Dirac structures on tori and prove that $O(n,n|\mathbb {Z})$-equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.

Détail

Publié le : 2004-01-01

MR 2127858 | Zbl 1068.46044

DOI : https://doi.org/10.5802/aif.2059
Classification:  46L65,  81S10

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