Auslander Regularity of 𝑝-adic Distribution Algebras

Schmidt, Tobias

doi:10.1090/S1088-4165-08-00323-3

Auslander Regularity of $p$-adic Distribution Algebras
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by Tobias Schmidt

Represent. Theory 12 (2008), 37-57

DOI: https://doi.org/10.1090/S1088-4165-08-00323-3

Published electronically: February 6, 2008

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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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