Quantization and Morita equivalence for constant Dirac structures on tori
Annales de l'Institut Fourier, Volume 54 (2004) no. 5, p. 1565-1580

We define a C * -algebraic quantization of constant Dirac structures on tori and prove that O(n,n|)-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|) 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.

DOI : https://doi.org/10.5802/aif.2059
Classification:  46L65,  81S10
Keywords: Dirac structure, Poisson structure, Morita equivalence, quantization
@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 = {aif.centre-mersenne.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. https://aif.centre-mersenne.org/item/AIF_2004__54_5_1565_0/

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