Characterizations by automorphism groups of some rank 3 buildings - II: A half strongly-transitive locally finite triangle building is a Bruhat-Tits building
locally finite triangle building; Bruhat-Tits building; Hjelmslev plane; strongly-transitive groups
Abstract :
[en] We complete the proof of the fact that every locally finite triangle building Delta with a half strongly-transitive automorphism group G (e.g., this happens when Delta is defined via a (B, N)-pair in G) is a Bruhat-Tits building associated with a classical linear group over a locally finite local skewfield.
Disciplines :
Mathematics
Author, co-author :
Van Maldeghem, H.
Van Steen, Kristel ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Bioinformatique
Language :
English
Title :
Characterizations by automorphism groups of some rank 3 buildings - II: A half strongly-transitive locally finite triangle building is a Bruhat-Tits building
Baker C., Lane N. D. and Lorimer J. W.: The Artin-Zorn theorem for finite punctually cohesive projective Klingenberg planes, Ars Combin. 29 (1990), 143-149.
Baker C., Lane N. D. and Lorimer J. W.: Local alternative rings and finite alternative right chain rings, C.R. Math. Rep. Acad. Sci. Canada 12 (1990).
Baker C., Lane N. D. and Lorimer J. W.: An affine characterization of Moufang projective Klingenberg planes, Res. in Math. 17 (1990).
Bruhat F. and Tits J.: Groupes réductifs sur un corps local. I. Données radicielles valuées, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5-252.
Hughes D. R. and Piper F. C.: Projective Planes, Springer, Berlin, 1973.
Huppert B.: Endliche Gruppen I, Springer-Verlag, Berlin, Heidelberg, New York, 1967.
Tits J.: Immeubles de type affine, In: L. Rosati (ed.) Buildings and the Geometry of Diagrams, Lecture Notes in Mathematics 1181, Springer, Berlin, 1986, pp. 159-190.
Van Maldeghem H.: On locally finite alternative division rings with valuation, J. Geometry 30 (1987), 42-48.
Van Maldeghem H.: Valuations on PTR's induced by triangle buildings, Geom. Dedicata 26 (1988), 29-84.
Van Maldeghem H.: Automorphisms of non-classical triangle buildings, Tijdsch. BeIg. Wisk. Gen. 42 (1990), 201-237.
Van Maldeghem H. and Van Steen K.: Characterizations by automorphisms of some rank 3 buildings, I. Some properties of half strongly-transitive triangle buildings, Preprint.
Van Steen K.: Non-spherical Tits-buildings of rank 3, PhD thesis, University of Ghent, 1996.