The center conjecture for thick spherical buildings
نویسنده
چکیده
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.
منابع مشابه
M ay 2 00 9 The center conjecture for spherical buildings of types F 4 and E 6 Bernhard
We prove that a convex subcomplex in a spherical building of type F4 or E6 is a subbuilding or the building automorphisms preserving the subcomplex fix a point on it. Our approach is differential-geometric and based on the theory of metric spaces with curvature bounded above.
متن کاملNo : 19 Title : ‘ the Strong Centre Conjecture : an Invariant Theory Approach
The aim of this note is to describe an approach to a strong form of J. Tits’ Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental result of G.R. Kempf from Geometric Invariant Theory and by interpreting this generalization in the context of spherical buildings. We are able to recapture the conjecture entirely in terms of our generalization of Kempf’s not...
متن کاملAutomorphisms of Non-spherical Buildings Have Unbounded Displacement
If φ is a nontrivial automorphism of a thick building ∆ of purely infinite type, we prove that there is no bound on the distance that φ moves a chamber. This has the following group-theoretic consequence: If G is a group of automorphisms of ∆ with bounded quotient, then the center of G is trivial.
متن کاملAutomorphisms 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...
متن کاملFluidity Onset Analysis in FG Thick-Walled Spherical Tanks under Concurrent Pressure Loading and Heat Gradient
In this paper,fluidity onset analysis in FG thick-walled spherical tanks under concurrent pressure loading and heat gradient has been presented. Designing thick-walled spherical tanks under pressure as tanks holding fluids under heat loads with high heat gradients require new approaches. Under high internal pressure and high temperature, the tank enters the plastic stage in a part of its thickn...
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 2009