On finite moore geometries

On Symmetric Moore Geometries

Moore Geometries ( Part Iv

For the relevant literature and most of the definitions and conventions the reader is referred to [1]. The next section contains an explicit description of the (reduced) characteristic polynomial of L4(s, t), and it is shown that this polynomial admits a decomposition into two closely related factors of degree 2 each. In Section 3 it is first shown that at least one of these factors must be red...

Fully packed loop models on finite geometries

A fully packed loop (FPL) model on the square lattice is the statistical ensemble of all loop configurations, where loops are drawn on the bonds of the lattice, and each loop visits every site once [4,18]. On finite geometries, loops either connect external terminals on the boundary, or form closed circuits, see for example Figure 1. In this chapter we shall be mainly concerned with FPL models ...

Finite Field Theory on Noncommutative Geometries

The propagator is calculated on a noncommutative version of the flat plane and the Lobachevsky plane with and without an extra (euclidean) time parameter. In agreement with the general idea of noncommutative geometry it is found that the limit when the two ‘points’ coincide is finite and diverges only when the geometry becomes commutative. The flat 4-dimensional case is also considered. This is...

Note on Lie algebras , finite groups and finite geometries

The subject of this note began with Thompson [Thl,2]. In the course of constructing his simple group Th, he considered the Lie algebra Lover iC of type Es. He constructed a decomposition L H1 ..L ... ..L H31 using a family H. {H1, ... , H31 } of Cartan algebras that are pairwise perpendicular with respect to the Killing form (he called this a "Dempwolff decomposition" of L; the construction was...