Tits Pentagons and the Root System $GH_2$

Bernhard Mühlherr; Richard Weiss

doi:10.4134/JKMS.j230350

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2024; 61(6): 1095-1126

Online first article October 16, 2024 Printed November 1, 2024

https://doi.org/10.4134/JKMS.j230350

Tits Pentagons and the Root System $GH_2$

Bernhard Mühlherr, Richard M. Weiss

Universit\"at Giessen; Tufts University

Abstract

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Abstract

We show that under a mild thickness condition, every Tits pentagon arises through a folding process from a free module of rank~$5$ over a unitary associative ring of stable range~$1$.

Keywords: Building, Tits polygon, stable range

MSC numbers: Primary 20E42; Secondary 51E24

Supported by: The work of the first author was partially supported by DFG Grant MU1281/7-1 and the work of the second author was partially supported by Simons Foundation Collaboration Grant 516364.