ar X iv : m at h / 04 11 12 9 v 1 [ m at h . Q A ] 6 N ov 2 00 4 NORMAL HOPF SUBALGEBRAS , DEPTH TWO AND GALOIS EXTENSIONS
نویسنده
چکیده
Let S be the left R-bialgebroid of a depth two extension with cen-tralizer R. We show that the left endomorphism ring of depth two extension, not necessarily balanced, is a left S-Galois extension of A op. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We also characterize weak Hopf-Galois extensions using an alternate Galois canonical mapping with the corollary that these are depth two.
منابع مشابه
ar X iv : m at h / 04 11 12 9 v 2 [ m at h . Q A ] 1 D ec 2 00 4 NORMAL HOPF SUBALGEBRAS , DEPTH TWO AND GALOIS EXTENSIONS
Let S be the left R-bialgebroid of a depth two extension with cen-tralizer R. We show that the left endomorphism ring of depth two extension, not necessarily balanced, is a left S-Galois extension of A op. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We find a class of examples of the alternative Hopf algebroids in...
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