%0 Journal Article
%T Finitary Galois extensions over noncommutative bases
%A I. Balint
%A K. Szlachanyi
%J Mathematics
%D 2004
%I arXiv
%X We study Galois extensions Coinv(M)<M for M an H-comodule algebra and H a Frobenius Hopf algebroid. We obtain generalizations of various theorems in Hopf-Galois theory by Kreimer-Takeuchi, Doi-Takeuchi and Cohen-Fischman-Montgomery. An algebra extension is Galois precisely if it is balanced, depth 2, and Frobenius. Then we show that Yetter-Drinfeld categories over H are always braided and their braided commutative algebras play the role of noncommutative scalar extensions by the Brzezinski-Militaru Theorem. Contravariant "fiber functors" are used to prove an analogue of Ulbrich's Theorem and to get a monoidal embedding of the category of modules over the endomorphism Hopf algebroid E=End(_N M_N).
%U http://arxiv.org/abs/math/0412122v1