Email Gateway (Aug 22 2022 at 13:40): Email Gateway (Aug 22 2022 at 13:40):From: Gerwin Klein <Gerwin.Klein@nicta.com.au>
A new AFP entry is online at https://www.isa-afp.org
Chamber Complexes, Coxeter Systems, and Buildings
by Jeremy Sylvestre
We provide a basic formal framework for the theory of chamber complexes and Coxeter systems, and for buildings as thick chamber complexes endowed with a system of apartments. Along the way, we develop some of the general theory of abstract simplicial complexes and of groups (relying on the group_add class for the basics), including free groups and group presentations, and their universal properties. The main results verified are that the deletion condition is both necessary and sufficient for a group with a set of generators of order two to be a Coxeter system, and that the apartments in a (thick) building are all uniformly Coxeter.
https://www.isa-afp.org/entries/Buildings.shtml
Enjoy!
Gerwin
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