A Schneider type theorem for hopf algebroids

JOURNAL OF ALGEBRA

卷:318

Article

Ardizzoni, A.²  Boehm, G.¹  Menini, C.² 

[1] Res Inst Particle & Nucl Phys, H-1525 Budapest, Hungary

[2] Univ Ferrara, Dept Math, I-44100 Ferrara, Italy

关键词: relative separable functors;    relative injective comodule algebras;    Hopf algebroids;    Galois extensions;   

DOI  :  10.1016/j.jalgebra.2007.05.017

来源: Elsevier

【 摘 要 】

Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B subset of 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 B subset of 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. (c) 2007 Elsevier Inc. All rights reserved.

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