Projective representations II. generalized chain geometries

Projective Representations II. Generalized chain geometries

In this paper, projective representations of generalized chain geometries are investigated, using the concepts and results of [5]. In particular, we study under which conditions such a projective representation maps the chains of a generalized chain geometry Σ(F,R) to reguli; this mainly depends on how the field F is embedded in the ring R. Moreover, we determine all bijective morphisms of a ce...

Projective Representations II. Generalized chain geometries

Projective geometries in exponentially dense matroids. II

We show for each positive integer a that, if M is a minor-closed class of matroids not containing all rank-(a+ 1) uniform matroids, then there exists an integer c such that either every rank-r matroid in M can be covered by at most r rank-a sets, or M contains the GF(q)-representable matroids for some prime power q and every rank-r matroid inM can be covered by at most cq rank-a sets. In the la...

Projective Representations of Generalized Symmetric Groups

Generalized projective geometries: general theory and equivalence with Jordan structures

In this work we introduce generalized projective geometries which are a natural generalization of projective geometries over a field or ring K but also of other important geometries such as Grassmannian, Lagrangian or conformal geometry (see [3]). We also introduce the corresponding generalized polar geometries and associate to such a geometry a symmetric space over K. In the finite-dimensional...