It is well known that a geometry belonging to a disconnected diagram is the direct sum of geometries corresponding to the connected components of the diagram. On the other hand, chamber systems with a disconnected diagram exist which do not split as direct products of components of smaller rank. Many finite examples of this kind are discussed in Groups of Lie Type and their Geometries (CUP, 1995, pp. 185-214), but none of them is simply connected. In this article, we construct a simply connected finite example.

Pasini, A. (1996). On a problem on chamber systems. GEOMETRIAE DEDICATA, 60(3), 225-236.

On a problem on chamber systems

PASINI, ANTONIO
1996

Abstract

It is well known that a geometry belonging to a disconnected diagram is the direct sum of geometries corresponding to the connected components of the diagram. On the other hand, chamber systems with a disconnected diagram exist which do not split as direct products of components of smaller rank. Many finite examples of this kind are discussed in Groups of Lie Type and their Geometries (CUP, 1995, pp. 185-214), but none of them is simply connected. In this article, we construct a simply connected finite example.
Pasini, A. (1996). On a problem on chamber systems. GEOMETRIAE DEDICATA, 60(3), 225-236.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/7204
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