Speaker: Anneleen De Schepper Affiliation: Ghent University Time: 13:00 Wednesday, 11 April, 2018 Location: 303-257 |
Traditionally, the Cayley-Dickson doubling process (CDDP) produces exactly the (non-singular) quadratic alternative algebras over a field K. A generalised version also yields singular quadratic alternative algebras. Starting from a field K, we go through all steps of the CDDP and have a look at the resulting algebras. The classical Veronesean map relates them to some interesting geometries. To obtain a general description of these geometries (without using the Veronesean map), we now start from a projective plane over K and successively apply a geometric analogue of the CDDP. In the non-singular case, the algebras can be captured as "quadratic and alternative" and the geometries as "characterised as a set of points and quadrics satisfying three axioms". The question remains whether this is also applies in the singular case, which clearly behaves in more complex ways. |