Morita equivalences between Hopf-Galois extensions. Applications.

Onderzoeksoutput: Meeting abstract (Book)Research


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.
Originele taal-2English
TitelAMS meeting #1048
StatusPublished - 5 apr 2009
EvenementUnknown -
Duur: 5 apr 2009 → …


Periode5/04/09 → …


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