Galois Theory of Hopf Galois Extensions

Details Galois Theory of Hopf Galois Extensions Galois Theory of Hopf Galois Extensions

2009-12-01

arxiv.org/abs/0912.0291v4

Mathematics

Quantum Algebra

Section 5 removed. Shorter lattice theoretic introduction. Same main results. Some statements are stated more clearly

Scientific paper

We introduce Galois Theory for Hopf-Galois Extensions proving existence of a Galois connection between subalgebras of an H-comodule algebra and generalised quotients of the Hopf algebra H. Moreover, we show that these quotients Q which define Q-Galois extension are the closed elements of our Galois connection. We generalise important results of Hopf--Galois Theory of M. Masuoka and H.-J. Schneider by showing that there is a bijective correspondence between right ideals coideals and right coideal subalgebras of any finite dimensional Hopf algebra and we reformulate the still open problem in the general (i.e. infinite dimensional) case. For cleft extensions we characterise closed elements of the Galois connection as Hopf-Galois extensions. We describe the relation of our results to the work of F. van Oystaeyen, Y. Zhang and also to the results of P. Schauenburg on biGalois extensions.

Affiliated with

Also associated with

No associations

Rating

Galois Theory of Hopf Galois Extensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Galois Theory of Hopf Galois Extensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Galois Theory of Hopf Galois Extensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-508113