2005/07/11 by Christian Kassel, Kassel, Christian · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.QA #msc:13B05 #msc:16W30 #msc:17B37 #msc:55R10 #msc:58B34 #msc:81R50 #msc:81R60
paper · pdf · doi:10.48550/arxiv.math/0507221
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
arxiv created 2005/07/11 · arxiv updated 2009/12/01
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.