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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Galois actions and blocks of tame infinitesimal group schemes


Authors: Rolf Farnsteiner and Andrzej Skowronski
Journal: Trans. Amer. Math. Soc. 359 (2007), 5867-5898
MSC (2000): Primary 16G70; Secondary 14L15, 16G20, 16G60, 16W20, 16W30, 17B50
Published electronically: July 20, 2007
MathSciNet review: 2336308
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Abstract: Given an infinitesimal group $ \mathcal{G}$, that is defined over an algebraically closed field of characteristic $ p \ge 3$, we determine the block structure of the algebra of measures $ H(\mathcal{G})$ in case its principal block $ \mathcal{B}_0(\mathcal{G})$ is tame and the height of the factor group $ \mathcal{G}/\mathcal{M}(\mathcal{G})$ of $ \mathcal{G}$ by its multiplicative center $ \mathcal{M}(\mathcal{G})$ is at least two. Our results yield a complete description of the stable Auslander-Reiten quiver of $ H(\mathcal{G})$ along with a criterion for the domesticity of $ H(\mathcal{G})$.


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Additional Information

Rolf Farnsteiner
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
Email: rolf@mathematik.uni-bielefeld.de

Andrzej Skowronski
Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Email: skowron@mat.uni.torun.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04124-4
PII: S 0002-9947(07)04124-4
Received by editor(s): November 15, 2004
Received by editor(s) in revised form: July 25, 2005
Published electronically: July 20, 2007
Additional Notes: This work was supported by Polish Scientific Grant KBN No. 1 PO3A 018 27
Article copyright: © Copyright 2007 American Mathematical Society