AUTOMORPHISMS AND OPPOSITION IN TWIN BUILDINGS
نویسندگان
چکیده
منابع مشابه
Automorphisms and Opposition in Twin Buildings
We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore, we show that no automorphism of a locally finite 2spherical twin building of rank at least 3 maps every residue of one fixed type to an opposite (a key step in the proof is showing that every duality of a thick finite projective plane admits an abs...
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In this paper, we characterize the natural opposition relation on the set of flags of a generalized polygon. We also investigate when a certain relation on any rank 2 geometry of finite diameter is equivalent to the opposition relation in a generalized polygon. As a consequence we obtain a new definition of generalized polygons. Finally, we also characterize the opposition relation in twin tree...
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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...
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It is well known that each compact orientable surface R gives rise to a simplicial complex C(R) playing in the theory of Teichmüller modular groups a role similar to the role of Tits buildings in theories of algebraic and arithmetic groups. In this paper we introduce, for each closed orientable surface S, an analogue of Tits buildings more suitable for investigation of the Torelli group I(S) of...
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In this paper, we define twinnings for affine R-buildings. We thus extend the theory of simplicial twin buildings of affine type to the non-simplicial case. We show how classical results can be extended to the non-discrete case, and, as an application, we prove that the buildings at infinity of aMoufang twin R-building have the induced structure of aMoufang building. The latter is not true for ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2013
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788712000481