Activities per year
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$$B$Hopf bimodules is equivalent to the category
of modules over the cotensor product of $A$ and $B^{\rm op}$. We present
applications to the MiyashitaUlbrich actions and to Hopf subalgebras.
As another application, we present a Hopf algebra version of an exact sequence
due to Beattie and del Rio, connecting the graded Picard group of a strongly graded
ring, and the stable part of the Picard group of its part of degree zero.
$A^{{\rm co}H}$ and $B^{{\rm co}H}$ are connected by a strict Morita context.
We investigate when this Morita context can be lifted to a Morita context between
$A$ and $B$. To this end, we present a Structure Theorem for Hopf bimodules: the
category of $A$$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 MiyashitaUlbrich 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 

Title of host publication  AMS meeting #1048 
Publication status  Published  5 Apr 2009 
Event  Unknown  Duration: 5 Apr 2009 → … 
Conference
Conference  Unknown 

Period  5/04/09 → … 
Keywords
 Morita context
Fingerprint
Dive into the research topics of 'Morita equivalences between HopfGalois extensions. Applications.'. Together they form a unique fingerprint.Activities
 2 Talk or presentation at a conference

AMS meeting #1048
Joost Vercruysse (Speaker)
4 Apr 2009 → 5 Apr 2009Activity: Talk or presentation › Talk or presentation at a conference

AMS meeting #1048
Stefaan Caenepeel (Speaker)
4 Apr 2009 → 5 Apr 2009Activity: Talk or presentation › Talk or presentation at a conference