Difference algebraic groups

Difference algebraic groups can be described as subgroups of the general linear group defined by algebraic difference equations in the matrix entries. They occur naturally as Galois groups in certain Galois theories and have applications to arithmetic problems. The main goal of this project is to further develop the very rich and beautiful theory of these groups and to expand their areas of application.

Algebraic groups can be described as subgroups of the general linear group defined by algebraic equations in the matrix entries. They play an important role in algebraic geometry and representation theory and have a well-developed structure theory. This project is at the crossroads of the theory of algebraic groups and difference algebra, i.e., the systematic study of difference equations from an algebraic point of view.

A substantial body of results is already available for difference algebraic groups defined by ordinary difference equations. A main theme of this project is to generalize these results to partial difference equations.