Algebraic Groups RWTH Aachen , WS 2006 Jürgen

Algebraic groups are analogues of the classical Lie groups, such as the linear, orthogonal or symplectic groups, over arbitrary algebraically closed fields. Hence they are no longer classical manifolds, but varieties in the sense of algebraic geometry. In particular, they are used in the uniform description of the finite groups of Lie type, which encompass a substantial part of all finite simple groups. Subject of the lecture is an introduction to linear algebraic groups. Here, tools both from group theory as well as from algebraic geometry come into play.