E 23

To any nonsingular symmetric or skew-symmetric bilinear form we can associate an involution on a split central simple algebra. This gives us a correspondence that allows us to study involutions on split algebras by using the well developed theory of quadratic and bilinear forms. One aim in the current study of algebras with involution is to find field extensions which split the algebra, but which do not alter certain properties of the involution, so that these properties may be studied using bilinear forms. In this talk we will show that in characteristic 2 the isotropy behaviour of involutions (of the first kind) when passing to a splitting field can be found in a relatively elementary manner. To do this we apply a refined version of Witt`s decomposition theorem for hermitian forms.

Dr. Andrew Dolphin

Universität Konstanz