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The Quarterly Journal of Mathematics Advance Access published online on March 28, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han038
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

THE GRADED CENTER OF THE STABLE CATEGORY OF A BRAUER TREE ALGEBRA

Radha Kessar{dagger} and Markus Linckelmann

Department of Mathematical Sciences, Meston Building, Aberdeen, AB24 3UE, UK

{dagger} Corresponding author. E-mail: kessar{at}maths.abdn.ac.uk

Received 24 June 2008;
  Abstract

We calculate the graded center of the stable category of a Brauer tree algebra. The canonical map from the Tate analogue of Hochschild cohomology to the graded center of the stable category is shown to induce an isomorphism module taking quotients by suitable nilpotent ideals. More precisely, we show that this map is surjective with nilpotent kernel in even degrees, while this map need not be surjective in odd degrees in general.


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