On Tits Buildings of Type A

Enumerating A3(2) Blueprints, and an Application

1. Definitions 2. Enumerating Blueprints 3. Applications References We present an enumeration scheme for all blueprints of an A2(p) building (with p prime). We then provide a computer based proof that the e An(Q 2) buildings do not conform to a blueprint for n 3. J. Tits ([1955b; 1955a; 1956]; see the introduction of [Tits 1974] for a historical discussion) introduced buildings in an attempt to...

Moufang Buildings and Twin Buildings

The “Moufang Condition” for spherical buildings was introduced by J. Tits in the appendix of [9], as a tool to give more structure to the classification of spherical buildings of rank at least three (which are automatically “Moufang”). More recently, also the spherical buildings of rank 2 satisfying the Moufang Condition are classified [13]. Hence one could say that, on the geometric level, sph...

Bruhat-tits Buildings and Analytic Geometry

This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry can be used to compactify buildings. We discuss in detail the example of the special linear group. Moreover, we give an intrinsic description of Bruhat-Tits buildings in the framework of non-Archim...

The center conjecture for thick spherical buildings

We prove that a convex subcomplex of a spherical building of type E7 or E8 is a subbuilding or the group of building automorphisms preserving the subcomplex has a fixed point in it. Together with previous results of Mühlherr-Tits, and Leeb and the author, this completes the proof of Tits’ Center Conjecture for thick spherical buildings.

Ramunajan (n1,n2,...,nd−1)-regular hypergraphs based on Bruhat-Tits Buildings of type Ãd−1 Contents

A reduction of axioms

Jacques Tits introduced the notion of a building as a geometry associated to groups of Lie type in [T1], providing new geometries associated to the exceptional groups of Lie type. In 1972, F. Bruhat and Tits [BT] developed a theory of affine buildings for the purpose of studying groups over fields having a discrete valuation, although their work applied more generally to groups over fields havi...