Abstract:

I will discuss two concepts of generalized Bratteli diagrams: discrete and measurable. A Bratteli diagram can be viewed as an infinite graded graph whose vertices are partitioned into finite levels, and edges between vertices exist only if they belong to neighboring levels. In my talk, I will consider Bratteli diagrams of two types: with countably infinite levels and uncountable levels represented by standard Borel spaces. It will be shown that these two approaches have many common properties and can be considered as parallel theories. We will discuss several particular classes of generalized Bratteli diagrams with interesting and important properties.

The talk is based on the results proved jointly with P. Jorgensen, O. Karpel, and S. Sanadhya.