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On quasi-classical limits of DQ-algebroids

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  19 January 2017

Paul Bressler ,
Alexander Gorokhovsky ,
Ryszard Nest  and
Boris Tsygan
Paul Bressler
Affiliation:
Departamento de Matemáticas, Universidad de Los Andes, Bogotá, Colombia email paul.bressler@gmail.com
Alexander Gorokhovsky
Affiliation:
Department of Mathematics, UCB 395, University of Colorado, Boulder, CO 80309-0395, USA email Alexander.Gorokhovsky@colorado.edu
Ryszard Nest
Affiliation:
Department of Mathematics, Copenhagen University, Universitetsparken 5, 2100 Copenhagen, Denmark email rnest@math.ku.dk
Boris Tsygan
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA email b-tsygan@northwestern.edu
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Abstract

We determine the additional structure which arises on the classical limit of a DQ-algebroid.

Keywords

algebroiddeformation quantizationclassical limit

MSC classification

Primary: 53D55: Deformation quantization, star products
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 1 , January 2017 , pp. 41 - 67
Copyright
© The Authors 2017 

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References

Baranovsky, V., Ginzburg, V., Kaledin, D. and Pecharich, J., Quantization of line bundles on Lagrangian subvarieties , Selecta Math. (N.S.) 22 (2016), 1–25.Google Scholar
Bertelson, M., Cahen, M. and Gutt, S., Equivalence of star products. Geometry and physics , Classical Quantum Gravity 14 (1997), A93–A107.Google Scholar
Bressler, P., Gorokhovsky, A., Nest, R. and Tsygan, B., Deformation quantization of gerbes , Adv. Math. 214 (2007), 230–266.CrossRefGoogle Scholar
Bressler, P., Gorokhovsky, A., Nest, R. and Tsygan, B., Formality theorem for gerbes , Adv. Math. 273 (2015), 215–241.Google Scholar
Brylinski, J.-L., Loop spaces, characteristic classes and geometric quantization, Progress in Mathematics, vol. 107 (Birkhäuser, Boston, MA, 1993).CrossRefGoogle Scholar
Bursztyn, H., Poisson vector bundles, contravariant connections and deformations , Progr. Theoret. Phys. Suppl. (2001), 26–37; Noncommutative geometry and string theory (Yokohama, 2001).Google Scholar
Bursztyn, H., Semiclassical geometry of quantum line bundles and Morita equivalence of star products , Int. Math. Res. Not. IMRN 2002 (2002), 821–846.CrossRefGoogle Scholar
Bursztyn, H. and Waldmann, S., Bimodule deformations, Picard groups and contravariant connections , K-Theory 31 (2004), 1–37.Google Scholar
Deligne, P., La formule de dualite globale (Springer, Berlin, 1973), 481–587.Google Scholar
Fischer, H. R. and Williams, F. L., Complex-foliated structures. I. Cohomology of the Dolbeault–Kostant complexes , Trans. Amer. Math. Soc. 252 (1979), 163–195.CrossRefGoogle Scholar
Kashiwara, M., Quantization of contact manifolds , Publ. Res. Inst. Math. Sci. 32 (1996), 1–7.CrossRefGoogle Scholar
Kashiwara, M. and Schapira, P., Deformation quantization modules, Astérisque, vol. 345 (Société Mathématique de France, 2012).Google Scholar
Kontsevich, M., Deformation quantization of algebraic varieties , Lett. Math. Phys. 56 (2001), 271–294; Euro Conférence Moshé Flato 2000, Part III (Dijon).CrossRefGoogle Scholar
Kostant, B., Quantization and unitary representations. I. Prequantization , in Lectures in modern analysis and applications, III, Lecture Notes in Mathematics, vol. 170 (Springer, Berlin, 1970), 87–208.Google Scholar
Mackenzie, K. C. H., General theory of Lie groupoids and Lie algebroids, London Mathematical Society Lecture Note Series, vol. 213 (Cambridge University Press, Cambridge, 2005).Google Scholar
Milne, J. S., Gerbes and abelian motives, Preprint (2003), arXiv:math/0301304.Google Scholar
Rawnsley, J. H., On the cohomology groups of a polarisation and diagonal quantisation , Trans. Amer. Math. Soc. 230 (1977), 235–255.Google Scholar
Vey, J., Déformation du crochet de Poisson sur une variété symplectique , Comment. Math. Helv. 50 (1975), 421–454.Google Scholar