Institut für Mathematik

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FS 21
Lie groupoids in geometry and physics
Mi 10.15 - 12.00 Raum: Y36M37 Plätze:

Wednesday 10-12, in 36 M 37. Tentative list of topics to be covered:
Introductory lectures by Dr I. AndroulidakisOverview of Lie groups and Lie algebras. Vector bundles, principal bundles, connection theory. Lie groupoids, Lie algebroids, differentiation, exponential map.
The transitive case Equivalence of transitive groupoids with principal bundles and formulation of the connection theory in terms of Lie algebroids Classification of transitive Lie algebroids The obstruction to the integrability of transitive Lie algebroids Geometric prequantization of symplectic manifolds and the integrability of transitive Lie algebroids
General groupoidsFoliations and groupoids Duality between Lie algebroids and Poisson manifolds Integrability of general Lie algebroids and quantization of Poisson manifoldsOnce the above material is covered, we may consider to extend further, to topics such as the role of groupoids in deformation-quantization and in noncommutative geometry.
ReferencesKirill Mackenzie. The general theory of Lie groupoids and Lie algebroids. Ana Cannas da Silva and Alan Weinstein. Geometric models for Noncommutative Algebras. R. Abraham and J. E. Marsden. Foundations of Mechanics.

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