Morita equivalences between Hopf-Galois extensions. Applications.

Research output: Chapter in Book/Report/Conference proceedingMeeting abstract (Book)

Abstract

Let $A$ and $B$ be two Hopf algebra extensions, and suppose that
$A^{{\rm co}H}$ and $B^{{\rm co}H}$ are connected by a strict Morita context.
We investigate when this Morita context can be lifted to a Morita context between
$A$ and $B$. To this end, we present a Structure Theorem for Hopf bimodules: the
category of $A$-$B$-Hopf bimodules is equivalent to the category
of modules over the cotensor product of $A$ and $B^{\rm op}$. We present
applications to the Miyashita-Ulbrich actions and to Hopf subalgebras.
As another application, we present a Hopf algebra version of an exact sequence
due to Beattie and del Rio, connecting the graded Picard group of a strongly graded
ring, and the stable part of the Picard group of its part of degree zero.
Original languageEnglish
Title of host publicationAMS meeting #1048
Publication statusPublished - 5 Apr 2009
EventUnknown -
Duration: 5 Apr 2009 → …

Conference

ConferenceUnknown
Period5/04/09 → …

Keywords

  • Morita context

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  • AMS meeting #1048

    Joost Vercruysse (Speaker)

    4 Apr 20095 Apr 2009

    Activity: Talk or presentationTalk or presentation at a conference

  • AMS meeting #1048

    Stefaan Caenepeel (Speaker)

    4 Apr 20095 Apr 2009

    Activity: Talk or presentationTalk or presentation at a conference

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