We define a -algebraic quantization of constant Dirac structures on tori and prove that -equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.
Nous définissons une quantification -algebrique des structures de Dirac constantes sur les tores, et nous démontrons que l’équivalence à 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.
Tang, Xiang ; Weinstein, Alan 1
@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}, pages = {1565--1580}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {5}, year = {2004}, doi = {10.5802/aif.2059}, zbl = {1068.46044}, mrnumber = {2127858}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2059/} }
TY - JOUR AU - Tang, Xiang AU - Weinstein, Alan TI - Quantization and Morita equivalence for constant Dirac structures on tori JO - Annales de l'Institut Fourier PY - 2004 SP - 1565 EP - 1580 VL - 54 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2059/ DO - 10.5802/aif.2059 LA - en ID - AIF_2004__54_5_1565_0 ER -
%0 Journal Article %A Tang, Xiang %A Weinstein, Alan %T Quantization and Morita equivalence for constant Dirac structures on tori %J Annales de l'Institut Fourier %D 2004 %P 1565-1580 %V 54 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2059/ %R 10.5802/aif.2059 %G en %F 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/articles/10.5802/aif.2059/
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