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Block representation type of reduced enveloping algebras


Authors: Iain Gordon and Alexander Premet
Journal: Trans. Amer. Math. Soc. 354 (2002), 1549-1581
MSC (2000): Primary 20G05; Secondary 17B20
DOI: https://doi.org/10.1090/S0002-9947-01-02826-4
Published electronically: December 7, 2001
MathSciNet review: 1873018
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Abstract: Let $K$ be an algebraically closed field of characteristic $p$, $G$ a connected, reductive $K$-group, $\mathfrak{g}=\text{Lie}(G)$, $\chi\in\mathfrak{g}^*$ and $U_\chi(\mathfrak{g})$ the reduced enveloping algebra of $\mathfrak{g}$ associated with $\chi$. Assume that $G^{(1)}$ is simply-connected, $p$ is good for $G$ and $\mathfrak{g}$ has a non-degenerate $G$-invariant bilinear form. All blocks of $U_\chi(\mathfrak{g})$ having finite and tame representation type are determined.


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Additional Information

Iain Gordon
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Email: ig@maths.gla.ac.uk

Alexander Premet
Affiliation: Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, England
Email: sashap@ma.man.ac.uk

DOI: https://doi.org/10.1090/S0002-9947-01-02826-4
Received by editor(s): July 24, 2000
Received by editor(s) in revised form: January 2, 2001
Published electronically: December 7, 2001
Additional Notes: The authors would like to thank the London Mathematical Society for supporting a visit of the first author to Manchester through a travel grant scheme. Further financial support for the first author was provided by TMR grant ERB FMRX-CT97-0100 at the University of Bielefeld.
Article copyright: © Copyright 2001 American Mathematical Society

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