Algebra Learning Seminar

Blake Madill, Department of Pure Mathematics, University of Waterloo

“GK Dimension and the Bergman Gap Theorem”

The Gelfand-Kirillov dimension (GK dimension) of a finitely generated k-algebra is a useful invariant which gives information about how far away an algebra is from being finite dimen- sional, how the growth of the algebra behaves, and in some cases generalizes the notion of transcendence degree. I will briefly motivate and define GK dimension and talk about which real numbers can be realized as the GK dimension of a finitely generated algebra. This will be done through many examples and a proof of the celebrated Bergman Gap Theorem.

MC 5479