Coherence of Augmented Iwasawa Algebras
James Timmins

TL;DR
This paper characterizes when augmented Iwasawa algebras of p-adic Lie groups are coherent, showing coherence occurs only for specific low-rank or solvable cases, with implications for classical groups.
Contribution
It provides a complete classification of coherence for augmented Iwasawa algebras of p-adic Lie groups based on root system rank and solvability.
Findings
Coherence occurs only for rank one root systems.
GL(n) has coherent augmented Iwasawa algebra iff n ≤ 2.
Certain solvable p-adic Lie groups have coherent augmented Iwasawa algebras.
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
