Quantization and Morita equivalence for constant Dirac structures on tori

Tang, Xiang; Weinstein, Alan

Tang, Xiang; Weinstein, Alan

Annales de l'Institut Fourier, Volume 54 (2004) no. 5, p. 1565-1580

Abstract
Résumé

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

Nous définissons une quantification $C^{*}$ -algebrique des structures de Dirac constantes sur les tores, et nous démontrons que l’équivalence à $O (n, n | ℤ)$ 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.

MR 2127858 | Zbl 1068.46044

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

@article{AIF_2004__54_5_1565_0,
     author = {Tang, Xiang and Weinstein, Alan},
     title = {Quantization and Morita equivalence for constant Dirac structures on tori},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {5},
     year = {2004},
     pages = {1565-1580},
     doi = {10.5802/aif.2059},
     zbl = {1068.46044},
     mrnumber = {2127858},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_5_1565_0}
}

Tang, Xiang; Weinstein, Alan. Quantization and Morita equivalence for constant Dirac structures on tori. Annales de l'Institut Fourier, Volume 54 (2004) no. 5, pp. 1565-1580. doi : 10.5802/aif.2059. http://www.numdam.org/item/AIF_2004__54_5_1565_0/

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