Spanning Point-line Geometries in Buildings of Spherical Type
نویسندگان
چکیده
In this paper, M denotes a Dynkin diagram defined over an index set I and (W, {ri}i∈I) will be the associated Coxeter system. The diagram M is called simply-laced if it has only single bonds. For any subset J ⊂ I, MJ denotes the subdiagram of M defined over J and WJ will be the subgroup of W having generator set {ri}i∈J . The pair (WJ , {ri}i∈J) then is a Coxeter system with diagram MJ . Let X be a building of type M , i.e. X is a chamber system over I such that each rank-one residue contains at least two chambers, and having a W -valued distance-function
منابع مشابه
Connectedness of Opposite-flag Geometries in Moufang Polygons
A generalized n-gon, n 2, is a rank 2 geometry whose incidence graph has diameter n and girth 2n, and each vertex has valency 3. If the latter condition is not satisfied , then we have a weak generalized n-gon. In this paper, we will always consider generalized n-gons with n 3 (generalized 2-gons are trivial geometries). They are the irreducible spherical buildings of rank 2. A generalized poly...
متن کاملThe center conjecture for thick spherical buildings
We prove that a convex subcomplex of a spherical building of type E7 or E8 is a subbuilding or the group of building automorphisms preserving the subcomplex has a fixed point in it. Together with previous results of Mühlherr-Tits, and Leeb and the author, this completes the proof of Tits’ Center Conjecture for thick spherical buildings.
متن کاملUniversal Covers of Geometries of Far Away Type
The geometries studied in this paper are obtained from buildings of spherical type by removing all chambers at non-maximal distance from a given element or flag. I consider a number of special cases of the above construction chosen among those which most frequently appear in the literature, proving that the resulting geometry is always simply connected but for three cases of small rank defined ...
متن کاملRoot shadow spaces
We give a characterization of the root shadow spaces of buildings whose types correspond to Dynkin diagrams. The results generalize earlier geometric point-line characterizations of certain spherical buildings as well as Timmesfeld’s characterization of abstract root subgroups.
متن کاملPoint-line characterizations of Lie geometries
There are two basic theorems. Let G be a strong parapolar space with these three properties: (1) For each point x and symplecton S, x is collinear to some point of S. (2) The set of points at distance at most two from a point forms a geometric hyperplane. (3) If every symplecton has rank at least three, every maximal singular subspace has finite projective rank. Then G is either D6; 6;A5; 3 or ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003