Gebäude Mathematik, 9. Etage, Raum 911

Orthogonal involutions can be thought of as twisted symmetric bilinear forms. Using this and the correspondence between symmetric bilinear forms and quadratic forms in characteristic different from two, we can consider the theory of quadratic forms over fields as embedded in the theory of algebras with involution. Pfister forms are a central part of the algebraic theory of quadratic forms, so it is natural to ask whether there is class of algebras with involution that acts as a generalisation of these forms. In characteristic two symmetric bilinear forms and quadratic forms are no longer equivalent. Quadratic pairs were introduced in order to give objects that correspond to quadratic forms in a way analogous to the correspondence between involutions and bilinear forms. One can again ask whether there is a class of quadratic pair generalising Pfister forms. In this talk we consider possible candidates for these Pfister involutions and Pfister quadratic pairs.

Dr. Andrew Dolphin

Universiteit Antwerpen