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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A bound on the complexity for $G_ rT$ modules
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by Daniel K. Nakano PDF
Proc. Amer. Math. Soc. 123 (1995), 335-341 Request permission

Abstract:

For group algebras the complexity of a module can be computed by looking at its restriction to elementary abelian subgroups. This statement is not true for modules over the restricted enveloping algebras of a restricted Lie algebra. Let G be a connected semisimple group scheme and ${G_r}$ be the rth Frobenius kernel. In this paper an upper bound on the complexity is provided for ${G_1}T$ modules. Furthermore, a bound is given for the complexity of a simple ${G_r}$ module, $L(\lambda )$, by the complexities of the simple ${G_1}$ modules in the tensor product decomposition of $L(\lambda )$.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 335-341
  • MSC: Primary 17B55; Secondary 17B50, 20G05
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1242099-7
  • MathSciNet review: 1242099