Proc. Summer school ''Geometric, topological and algebraic methods for quantum field theory'' (Villa de Leyva, Colombia, July 2015), in Quantization, Geometry and Noncommutative Structures in Mathematics and Physics, 75--133, Math. Phys. Stud., Springer, Cham, 2017; arXiv:1612.01821.

Christian Kassel

Principal fiber bundles in non-commutative geometry

Mathematics Subject Classification (2000): 16T05, 17B37, 55R10, 81R60, 81R50

Abstract. These are the expanded notes of a course given at the Summer school "Geometric, topological and algebraic methods for quantum field theory" held at Villa de Leyva, Colombia in July 2015. We first give an introduction to non-commutative geometry and to the language of Hopf algebras. We next build up a theory of non-commutative principal fiber bundles and consider various aspects of such objects. Finally, we illustrate the theory using the quantum enveloping algebra U_qsl(2) and related Hopf algebras.

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(28 novembre 2018)