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
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 find a class of examples of the alternative Hopf algebroids in [5]. We also characterize finite weak Hopf-Galois extensions using an alternate Galois canonical mapping with several corollaries: that these are depth two and that surjectivity of the Galois mapping implies its bijectivity.
منابع مشابه
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
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 alterna...
متن کاملar X iv : m at h . R A / 0 21 13 20 v 2 9 D ec 2 00 3 Sup - lattice 2 - forms and quantales ∗
A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.
متن کاملGalois Theory for Bialgebroids, Depth Two and Normal Hopf Subalgebras
We reduce certain proofs in [16, 11, 12] to depth two quasibases from one side only, a minimalistic approach which leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property. We prove that a proper algebra extension is a left T -Galois extension for some right finite projective left bialgebroid over some algebra R if and only if ...
متن کاملSemisimple Hopf Algebras and Their Depth Two Hopf Subalgebras
We prove that a depth two Hopf subalgebra K of a semisimple Hopf algebra H is normal (where the ground field k is algebraically closed of characteristic zero). This means on the one hand that a Hopf subalgebra is normal when inducing (then restricting) modules several times as opposed to one time creates no new simple constituents. This point of view was taken in the paper [13] which establishe...
متن کاملSome Topics On Braided Hopf Algebras And Galois Extension in Braided Tensor Categories
Braided Hopf algebras have attracted much attention in both mathematics and mathematical physics (see e.g. [2][4][14][16][17][18][20][23]). The classification of finite dimensional Hopf algebras is interesting and important for their applications (see [1] [24]). Braided Hopf algebras play an important role in the classification of finite-dimensional pointed Hopf algebras (e.g. [1][2] [21]). The...
متن کامل