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A Schneider type theorem for Hopf algebroids | | Alessandro Ardizzoni
; Gabriella Böhm
; Claudia Menini
; | | Date: |
21 Dec 2006 | | Subject: | Quantum Algebra; Rings and Algebras | | Abstract: | Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions Bsubseteq A by H, are studied. Assuming that a lifted canonical map is a split epimorphism of modules of the non-commutative base algebra of H, relative injectivity of the H-comodule algebra A is related to the Galois property of the extension Bsubseteq A and also to the equivalence of the category of relative Hopf modules to the category of B-modules. This extends a classical theorem by H.-J. Schneider on Galois extensions by a Hopf algebra. Our main tool is an observation that relative injectivity of a comodule algebra is equivalent to relative separability of a forgetful functor, a notion introduced and analysed hereby. | | Source: | arXiv, math/0612633 | | Services: | Forum | Review | PDF | Favorites | |
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