Van Maldeghem, H.; Van Steen, K. Moufang affine buildings have Moufang spherical buildings at infinity. (English) Zbl 0891.51007 Glasg. Math. J. 39, No. 3, 237-241 (1997). The Moufang condition for – not necessarily spherical – buildings was introduced by J. Tits [J. Algebra 105, 542-573 (1987; Zbl 0626.22013)]. It generalizes the usual Moufang condition for spherical buildings [see J. Tits, Atti dei Convegni Lincei 17, 229-246 (1976; Zbl 0347.50005)], which on its turn was a generalization of the Moufang condition for projective planes. The Moufang condition seems to be the most natural condition under which a classification of certain classes of buildings is possible. For spherical buildings of rank 2, Tits announces such classification and partial results have been published. In this note, it is shown that such a classification can be reduced to checking the Moufang property in the “known classical buildings”. The authors’ method uses the building at infinity of the affine building. The definition of Moufang affine building does not imply ipso facto that the building at infinity also satisfies the Moufang condition. It is shown that this is however a consequence. The main results read: The building at infinity of an irreducible Moufang rank 3 affine building is a Moufang rank 2 spherical building. The irreducible Moufang rank 3 affine buildings are amongst the affine buildings arising from an algebraic group of relative rank 2 defined over a field with discrete valuation (with respect to which the field is complete), which is invariant under the field involution that is possibly needed to define the group; also, the local field has equal characteristic. Reviewer: Serguey M.Pokas (Odessa) Cited in 3 Documents MSC: 51E24 Buildings and the geometry of diagrams Keywords:buildings; Moufang condition; apartments; Coxeter complexes; special vertexes; ray; sector; parallel walls; Hjelmslev-planes; Moufang polygons Citations:Zbl 0626.22013; Zbl 0347.50005 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1007/BF01324727 · Zbl 0659.51010 · doi:10.1007/BF01324727 [2] Maldeghem, n, Glasgow Math. J. 31 pp 257– (1989) [3] DOI: 10.1016/0021-8693(87)90214-6 · Zbl 0626.22013 · doi:10.1016/0021-8693(87)90214-6 [4] Ronan, Lectures on Buildings 7 (1989) [5] Tits, Atti dei Convegni Lincei 17 pp 229– (1976) [6] Tits, Buildings of spherical type and finite BN-pairs 386 (1974) · Zbl 0295.20047 [7] DOI: 10.1007/BFb0075514 · doi:10.1007/BFb0075514 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.