ABSTRACT

Actions and Invariants of Algebraic Groups presents a self-contained introduction to geometric invariant theory that links the basic theory of affine algebraic groups to Mumford's more sophisticated theory. The authors systematically exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify and compactify many of the rele

chapter 1|72 pages

Algebraic Geometry

chapter 2|34 pages

Lie algebras

chapter 3|24 pages

Algebraic groups: basic definitions

chapter 6|34 pages

Actions of algebraic groups

chapter 7|26 pages

Homogeneous spaces

chapter 9|28 pages

Reductivity

chapter 11|18 pages

Affine homogeneous spaces

chapter 12|30 pages

Hilbert’s 14th problem

chapter 13|30 pages

Quotients