Proc. Abel Centennial Conference, The Legacy of Niels Henrik Abel, The Abel Bicentennial, Oslo, 2002, O. A. Laudal, R. Piene (eds.), Springer-Verlag 2004, 737-748.

Christian Kassel

Quantum principal bundles up to homotopy equivalence

Mathematics Subject Classification (1991): 16W30, 55R10, 58B34, 81R50, 81R60

Abstract. Hopf Galois extensions are the algebraic analogues of principal bundles in noncommutative geometry. In this paper we introduce and discuss the concept of homotopy equivalence for Hopf Galois extensions. We examine the special case when the Hopf algebra is a Sweedler or a Taft Hopf algebra and determine the corresponding Hopf Galois extensions up to homotopy equivalence.

Erratum. On page 9, line 2 replace "H is commutative" by "the extension is commutative".

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(29 octobre 2004)