Actions and Invariants of Algebraic Groups

Walter Ferrer Santos is a professor of mathematics at the University of the Republic, Montevideo, Uruguay. Alvaro Rittatore is an associate professor of mathematics at the University of the Republic, Montevideo, Uruguay.

Algebraic geometry. Lie algebras. Algebraic groups: basic definitions. Algebraic groups: Lie algebras and representations. Algebraic groups: Jordan decomposition and applications. Actions of algebraic groups. Homogeneous spaces. Algebraic groups and Lie algebras in characteristic zero. Observable subgroups of affine algebraic groups. Observable actions of affine algebraic groups. Observable subgroups of affine monoids. Affine homogeneous spaces. Hilbert's 14th problem. Quotients. Appendix. Basic definitions and results.