# 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 language English AMS meeting #1048 Published - 5 Apr 2009 Unknown - Duration: 5 Apr 2009 → …

### Conference

Conference Unknown 5/04/09 → …

## 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