Pure Math Graduate Student Conference

Abstract

"R-Universal Central Extensions"

In this talk I will introduce a generalized concept of universal central extensions of groups, and explain how the classical theory can be seen as one instance of this larger homological theory. I will identify when a group G has an ``R-universal central extension" and recognition criteria for when a central extension of G is R-universal. Also I will briefly mention the idea of an R-universal central extension of a module and will discuss one application of this.