A Schneider type theorem for Hopf algebroids

A. Ardizzoni, G. Böhm, C. Menini

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Comodule algebras of a Hopf algebroid H with a bijective antipode, i.e. algebra extensions B ⊆ 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 ⊆ 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.

Original languageEnglish
Pages (from-to)225-269
Number of pages45
JournalJournal of Algebra
Volume318
Issue number1
DOIs
Publication statusPublished - Dec 1 2007

Fingerprint

Comodule
Algebra
Theorem
Injectivity
Module
Antipode
Epimorphism
Galois Extension
Bijective
Galois
Separability
Hopf Algebra
Functor
Equivalence

Keywords

  • Galois extensions
  • Hopf algebroids
  • Relative injective comodule algebras
  • Relative separable functors

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

A Schneider type theorem for Hopf algebroids. / Ardizzoni, A.; Böhm, G.; Menini, C.

In: Journal of Algebra, Vol. 318, No. 1, 01.12.2007, p. 225-269.

Research output: Contribution to journalArticle

Ardizzoni, A. ; Böhm, G. ; Menini, C. / A Schneider type theorem for Hopf algebroids. In: Journal of Algebra. 2007 ; Vol. 318, No. 1. pp. 225-269.
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