Algorithmic Invariant Theory
Gregor Kemper
Technische Universitaet Muenchen
Zentrum Mathematik - M11, Boltzmannstr. 3
85748 Garching, Germany
Phone: +49 89 289 17454, Fax: +49 89 289 17457
e-mail: kemper@ma.tum.de
http://www-m11.ma.tum.de/~kemper
Table of contents
- Invariant rings
- Finite generation
- Derksen's algorithm
- Noether's degree bound
- Separating invariants
Short Abstract
Invariant theory seeks to describe the set of all polynomial functions
which are constant on the orbits of a given group action, and studies
their capabilities of separating orbits. One of the factors that gave
new impetus to this classical subject was the emergence of new
computational methods and faster computers. Nowadays, invariant theory
is at the crossroads of algebraic geometry, computational commutative
algebra, and representation theory. In this tutorial we study the
classical questions of invariant theory and their relation to
computational issues. The topics will include finite generation,
Derksen's algorithm, degree bounds, and separating invariants.