Locally polar geometries with affine planes
نویسندگان
چکیده
The study of geometries on the absolute points of polarities in projective spaces has been started by Veldkamp [21], who was the first to give a synthetic characterization of these geometries, which he called polar spaces. As part of his work on spherical buildings [19], Tits extended Veldkamp’s results to a somewhat larger class of geometries related to pseudo-quadratic forms. In 1974, Buekenhout and Shult proved that most of the axioms used by Veldkamp and Tits can be deduced from the following beautiful axiom only involving points and lines, see [3]:
منابع مشابه
Realization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
متن کاملLocal Characterizations of Geometries
One of the best ways to understand the nature of finite simple groups is through geometries associated with them. This approach for classical and exceptional groups of Lie type has been quite successful and has led to the deveopment of the concept of buildings and polar spaces. The latter have been characterized by simple systems of axioms with a combinatorial-geometric flavour. It has been obs...
متن کاملBounding the size of certain rank 3 geometries with designs as rank 2 residues
We consider locally finite geometries of rank 3 belonging to certain diagrams where all strokes represent classes of non-trivial designs, at least one of them consisting of symmetric designs other than projective planes. The gonality diagram of such geometry is of spherical type, whereas the diameter diagram is of affine type. In cases like this, the criteria available from 24 cannot tell us an...
متن کاملShrinkings, structures at infinity and affine expansions, with an application to c-extended P- and T-geometries
This paper is a shortened exposition of the theory of shrinkings, with particular emphasis on the relations between shrinkings and geometries at infinity or affine expansions. To make things easier, we shall only consider locally affine geometries, referring the reader to [A. Pasini, C. Wiedorn, Local parallelisms, shrinkings and geometries at infinity, in: A. Pasini (Ed.), Topics in Diagram Ge...
متن کاملMubs, Polytopes, and Finite Geometries
A complete set of N + 1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p, where p is a prime number. They mesh naturally with finite affine planes of order N , that exist when N = p. The existence of MUBs for other values of N is an open question, and the same is true for finite affine planes. I explore the question whether the existence of complete sets of MUBs is dir...
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:
- Eur. J. Comb.
دوره 13 شماره
صفحات -
تاریخ انتشار 1992