Excellent Algebraic Groups, I Original Research Article

The notion of an excellent quadratic form has been introduced by M. Knebusch (Proc. London Math. Soc.33, 1976, 65–93;34, 1977, 1–31). It has an obvious analogue for a semisimple linear algebraic groupGover an arbitrary fieldk: the groupGis excellent if, for any field extensionKofk, the anisotropic kernel of theK-groupG ×k Kcan be defined by ak-group. The aim of this paper is to investigate excellence properties of special linear and orthogonal groups.