×

On polyhedra of rank 2. (Sur les polyèdres de rang 2.) (French) Zbl 0912.51005

Séminaire de théorie spectrale et géométrie. Année 1996-1997. St. Martin D’Hères: Univ. de Grenoble I, Institut Fourier, Sémin. Théor. Spectrale Géom., Chambéry-Grenoble. 15, 99-104 (1997).
This is a survey on \(\widetilde A_2\)-buildings with finite panels. The author mentions (without proof) various constructions of ‘exotic’ (i.e. non-Moufang) triangle buildings. Let \(q\) denote the cardinality of a typical panel. The smallest possible value is \(q=2\). In this case, the irreducible residues are Fano planes, so special arguments are needed to show that the building itself is non-Moufang. The author states the following result: there is an uncountable number of isomorphism types of \(\widetilde A_2\)-buildings with a fixed isomorphism type of distance-two balls.
For the entire collection see [Zbl 0882.00016].

MSC:

51E24 Buildings and the geometry of diagrams
PDFBibTeX XMLCite
Full Text: EuDML