Peter Symonds

The Module structure of a Group Action on a Ring

Consider a finite group G acting on a graded Noetherian k-algebra S, where k is a field of characteristic p; for example S might be a polynomial ring, in which case S is the symmetric algebra on a kG-module. Regard S as a graded kG-module and express it as a sum of indecomposable modules.

There are various questions we can now ask concerning a given isomorphism type of indecomposable kG-modules. Does it occur? If so, by which degree? How frequently does it occur? How many different isomorphism types occur? We show how this can be described in terms of homological algebra and how it is linked to the geometry of the group action on the spectrum of S.