Suppose Î“ is a Lie incidence geometry defined over some field F having a Lie incidence geometry Î“0 of the same type but defined over a subfield F0 â‰¤ F as a subgeometry. We investigate the followingâ€¦ (More)

In this paper, M denotes a Dynkin diagram defined over an index set I and (W, {ri}iâˆˆI) will be the associated Coxeter system. The diagram M is called simply-laced if it has only single bonds. For anyâ€¦ (More)

It is well known that, given a point-line geometry Î“ and a projective embedding Îµ : Î“ â†’ PG(V ), if dim(V ) equals the size of a generating set of Î“, then Îµ is not derived from any other embedding.â€¦ (More)

Let be the dual of a classical polar space and let e be a projective embedding of , defined over a commutative division ring. We shall prove that, if e is homogeneous, then it is polarized.

Exploiting the interplay between hyperbolic and isotropic geometry, we prove that the grassmannian of totally isotropic k-spaces of the polar space associated to the symplectic group Sp2n(F) hasâ€¦ (More)

Let B be a class of point-line geometries. Given Î“i âˆˆ B with subspace Si for i = 1, 2, does any isomorphism Î“1âˆ’S1 âˆ’â†’ Î“2âˆ’S2 extend to a unique isomorphism Î“1 âˆ’â†’ Î“2? It is known to be true if B is theâ€¦ (More)

The Curtis-Tits-Phan theory as laid out originally by Bennett and Shpectorov describes a way to employ Titsâ€™ lemma to obtain presentations of groups related to buildings as the universal completionâ€¦ (More)

Let n â‰¥ 3 and let F be a field of characteristic 2. Let DSp(2n, F) denote the dual polar space associated with the building of Type Cn over F and let Gnâˆ’2 denote the (n âˆ’ 2)-Grassmannian of type Cn.â€¦ (More)

Let n â‰¥ 3 and let F be a field of characteristic 2. Let DSp(2n, F) denote the dual polar space associated with the building of type Cn over F and let Gnâˆ’2 denote the (n âˆ’ 2)-Grassmannian of type Cn.â€¦ (More)