Locally split and locally finite twin buildings of 2-spherical type

by Bernhard Mühlherr

Abstract:
We prove a fixed point theorem for twin buildings of arbitrary rank. This theorem is then used to construct certain twin buildings whose existence was conjectured by J. Tits. As a consequence we obtain a classification of twin buildings whose rank 2 residues correspond to split algebraic groups over a field of cardinality at least 4. A similar result follows for twin buildings whose rank 2 residues are finite.

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1991 Mathematics Subject Classification: 51E24 .

To appear in: Journal für die reine und angewandte Mathematik

Contact: Bernhard.Muehlherr@Mathematik.Uni-Dortmund.DE