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

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