#### Vol. 17, No. 2, 2019

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On triples of ideal chambers in $A_2$-buildings

### Anne Parreau

Vol. 17 (2019), No. 2, 109–140
##### Abstract

We investigate the geometry in a real Euclidean building $X$ of type ${A}_{2}$ of some simple configurations in the associated projective plane at infinity $ℙ$, seen as ideal configurations in $X$, and relate it with the projective invariants (from the cross ratio on $ℙ$). In particular we establish a geometric classification of generic triples of ideal chambers of $X$ and relate it with the triple ratio of triples of flags.

##### Keywords
Euclidean buildings, projective planes, ideal configurations, triple ratio
Primary: 51E24
Secondary: 20E42