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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Block representation type of reduced enveloping algebras
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by Iain Gordon and Alexander Premet PDF
Trans. Amer. Math. Soc. 354 (2002), 1549-1581 Request permission

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
  • MR Author ID: 190461
  • Email: sashap@ma.man.ac.uk
  • 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.
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1873018