Quantum principal bundles up to homotopy equivalence
Abstract
Description
We translate some fundamental properties satisfied by topological principal bundles into the setting of Hopf-Galois extensions. The properties are: functoriality, homotopy, and triviality. The main new concept of the paper is the homotopy equivalence of Hopf-Galois extensions. We work in the particular case where the subalgebra of coinvariants is central but without any restriction on the Hopf algebras coacting on the quantum principal bundle. We examine in detail the case when the Hopf algebra is one of Sweedler or Taft's finite-dimensional Hopf algebras.
12 pages. This is a corrected version of a paper published in "The Legacy of Niels Henrik Abel", 737-748. O. A. Laudal, R. Piene (eds.), Springer-Verlag 2004
12 pages. This is a corrected version of a paper published in "The Legacy of Niels Henrik Abel", 737-748. O. A. Laudal, R. Piene (eds.), Springer-Verlag 2004