15/04/2010, 10:00 — 11:00 — Room P3.10, Mathematics Building Marcin Szamutolski, Instituto Superior Técnico
Galois theory of Hopf-Galois extensions
For a not necessarily commutative comodule algebra over a Hopf algebra, we construct a Galois correspondence between the complete lattices of of subalgebras and the complete lattice of generalised quotients of the structure Hopf algebra. The construction involves techniques of lattice theory and of Galois connections. Such a 'Galois Theory' generalises the classical Galois Theory for field extensions, and some important results of S.Chase and M.Sweedler, F. van Oystaeyen, P.Zhang and P.Schauenburg. Using the developed theory we positively answer the question raised by S. Montgomery: is there a bijective correspondence between generalised subobjects of a Hopf algebra and its generalised quotients? If time permits, I will present a proof, based on our results, for finite dimensional Hopf algebras. This is joint work with Dorota Marciniak (UAB Barcelona).
