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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Auslander Regularity of $p$-adic Distribution Algebras
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by Tobias Schmidt PDF
Represent. Theory 12 (2008), 37-57 Request permission

Abstract:

Given a compact $p$-adic Lie group over an arbitrary base field we prove that its distribution algebra is Fréchet-Stein with Auslander regular Banach algebras whose global dimensions are bounded above by the dimension of the group. As an application, we show that nonzero coadmissible modules coming from smooth or, more generally, $U(\mathfrak {g})$-finite representations have a maximal grade number (codimension) equal to the dimension of the group.
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Additional Information
  • Tobias Schmidt
  • Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
  • Address at time of publication: Département de Mathématiques, Bâtiment 425, Université Paris-Sud 11, F-91405 Orsay Cedex, France
  • Email: toschmid@math.uni-muenster.de
  • Received by editor(s): July 5, 2007
  • Published electronically: February 6, 2008
  • Additional Notes: The author was supported by a grant within the DFG Graduiertenkolleg “Analytische Topologie und Metageometric” at Münster
  • © Copyright 2008 American Mathematical Society
  • Journal: Represent. Theory 12 (2008), 37-57
  • MSC (2000): Primary 22E50; Secondary 11S99
  • DOI: https://doi.org/10.1090/S1088-4165-08-00323-3
  • MathSciNet review: 2375595