Year: 2018
Type: preprint
Abstract: Given a universal elementary Chevalley-Demazure group $E_Φ^{sc}(R)$ for which its (standard) parabolic subgroups are finitely generated, we consider the problem of classifying which parabolics $P(R) \subset E_Φ^{sc}(R)$ are finitely presented. We show that, under mild assumptions, this is equivalent to the finite presentability of a suitable retract of $P$ which contains the Levi factor. If the base ring $R$ is a Dedekind domain of arithmetic type, we combine our results with well-known theorems due to Borel-Serre, Abels, Behr and Bux to give a partial classification of finitely presentable $S$-arithmetic subgroups of parabolics in split reductive linear algebraic groups.
Source: arXiv (Cornell University)
Author: Rego, Yuri Santos
Institution: Bielefeld University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2783758893