"Biaffine geometries, amalgams and group recognition"

"Biaffine geometries, amalgams and group recognition"

Tue, 08/11/2011
17:00 		Dr Justin McInroy (Oxford) Algebra Seminar Add to calendar L2
"Biaffine geometries, amalgams and group recognition"
A polar space $ \Pi $ is a geometry whose elements are the totally isotropic subspaces of a vector space $ V $ with respect to either an alternating, Hermitian, or quadratic form. We may form a new geometry $ \Gamma $ by removing all elements contained in either a hyperplane $ F $ of $ \Pi $, or a hyperplane $ H $ of the dual $ \Pi^* $. This is a biaffine polar space. We will discuss two specific examples, one with automorphism group $ q^6:SU_3(q) $ and the other $ G_2(q) $. By considering the stabilisers of a maximal flag, we get an amalgam, or "glueing", of groups for each example. However, the two examples have "similar" amalgams - this leads to a group recognition result for their automorphism groups.