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arXiv · 2103.13765

Coherence of Augmented Iwasawa Algebras

James Timmins
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Abstract

The augmented Iwasawa algebra of a p-adic Lie group is a generalisation of the Iwasawa algebra of a compact p-adic Lie group. We prove that a split-semisimple group over a p-adic field has a coherent augmented Iwasawa algebra if and only if its root system is of rank one. We deduce that the general linear group of degree n has a coherent augmented Iwasawa algebra precisely when n is at most two. We also characterise when certain solvable p-adic Lie groups have a coherent augmented Iwasawa algebra.

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James Timmins. 2021-03-25. Coherence of Augmented Iwasawa Algebras. https://doi.org/10.1016/j.aim.2023.108916

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