The Module Structure of a Group Action on a Ring

Explore the intricate relationship between group actions and ring structures in this 49-minute lecture by Peter Symonds from the Hausdorff Center for Mathematics. Delve into the analysis of a finite group G acting on a graded Noetherian k-algebra S, where k is a field of characteristic p. Examine how S can be viewed as a kG-module and investigate the multiplicity of indecomposable modules as summands in each degree. Discover the connections between this module structure, homological algebra, and the geometric aspects of group actions on the spectrum of S. Gain insights into advanced algebraic concepts and their applications in understanding group actions on rings.