×
Waldmann, Stefan

The covariant Picard groupoid in differential geometry. (English) Zbl 1135.53061

Int. J. Geom. Methods Mod. Phys. 3, No. 3, 641-654 (2006).
The author studies the covariant Picard groupoid in the framework of differential geometry. Some general and important results exist in the study of Morita equivalence when a symmetry given by a Hopf algebra action is considered. In this paper, the author discusses these results from the differential geometric point of view. The paper starts with some recalls about the passage from algebraic frameworks to differential ones. The author discusses then the covariant aspects of Morita theory. Finally, a symmetry given by a Hopf algebra action is considered in the differential context and new results on the covariant Picard groupoid are found. Explicit computation of a certain part of the Lie algebra covariant Picard group is also obtained.
Reviewer: Angela Gammella-Mathieu (Metz)

Cited in 1 Document

MSC:

53D55 Deformation quantization, star products
16D90 Module categories in associative algebras

Keywords:

Morita equivalence; Picard groupoids; differential geometry; Hopf algebra actions
PDF BibTeX XML Cite
\textit{S. Waldmann}, Int. J. Geom. Methods Mod. Phys. 3, No. 3, 641--654 (2006; Zbl 1135.53061)
Full Text: DOI arXiv
  • logo of hbz
  • logo of WorldCat

References:

[1] DOI: 10.1023/A:1009958527372 · Zbl 0944.16005
[2] Bates S., Berkeley Mathematics Lecture Notes 8, in: Lectures on the Geometry of Quantization (1995)
[3] DOI: 10.1016/0003-4916(78)90224-5 · Zbl 0377.53024
[4] DOI: 10.1007/BFb0074299 · Zbl 1375.18001
[5] DOI: 10.1016/S0393-0440(00)00035-8 · Zbl 1039.46052
[6] DOI: 10.1007/s002200200657 · Zbl 1036.53068
[7] DOI: 10.1023/B:KTHE.0000021354.07931.64 · Zbl 1054.53101
[8] DOI: 10.2140/pjm.2005.222.201 · Zbl 1111.53071
[9] Bursztyn H., Moscow Math. J. 4 pp 39–
[10] Connes A., Noncommutative Geometry (1994)
[11] G. Dito and D. Sternheimer, Deformation Quantization, IRMA Lectures in Mathematics and Theoretical Physics 1, ed. G. Halbout (Walter de Gruyter, Berlin, New York, 2002) pp. 9–54.
[12] DOI: 10.1007/s00013-005-1268-3 · Zbl 1082.46020
[13] S. Gutt, Conférence Moshé Flato 1999. Quantization, Deformations, and Symmetries, Mathematical Physics Studies 21, eds. G. Dito and D. Sternheimer (Kluwer Academic Publishers, Dordrecht, Boston, London, 2000) pp. 217–254.
[14] DOI: 10.1016/j.jpaa.2005.07.015 · Zbl 1108.53056
[15] DOI: 10.1007/978-1-4612-0783-2
[16] DOI: 10.1007/BFb0079068 · Zbl 0223.53028
[17] DOI: 10.1007/978-1-4612-0525-8
[18] DOI: 10.1007/978-1-4612-1680-3
[19] DOI: 10.1007/978-1-4613-9719-9_14
[20] DOI: 10.1017/CBO9780511615450
[21] Morita K., Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 pp 83–
[22] DOI: 10.1090/S0002-9939-05-07979-7 · Zbl 1077.58005
[23] DOI: 10.2307/2372901 · Zbl 0104.17703
[24] Rieffel M. A., J. Pure. Appl. Math. 5 pp 51–
[25] DOI: 10.1007/978-3-0348-7469-4
[26] DOI: 10.2307/1970310 · Zbl 0116.40502
[27] DOI: 10.1090/S0002-9947-1962-0143225-6
[28] DOI: 10.1007/s11005-004-0421-4 · Zbl 1065.53070
[29] DOI: 10.1142/S0129055X05002297 · Zbl 1138.53316
[30] DOI: 10.1007/BF02099098 · Zbl 0746.58034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.