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Auslander Regularity of $p$-adic Distribution Algebras

Author: Tobias Schmidt
Journal: Represent. Theory 12 (2008), 37-57
MSC (2000): Primary 22E50; Secondary 11S99
Published electronically: February 6, 2008
MathSciNet review: 2375595
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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

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
Article copyright: © Copyright 2008 American Mathematical Society