Operator Algebra Seminar

Speaker:  Anatoly Vershik (St. Petersburg)

Title: The theory of traces on AF-algebras and standard filtrations.

Abstract : Inductive limits of finite dimensional *-algebras and the corresponding  AF-algebras must be considered not only as inductive limit, but also from the point of view of theory of filtrations - the theory of decreasing sequences of the commutative subalgebras (tail filtration of Gelfand-Zetlin subalgebras). It means that we have to study the asymptotics of the space of paths of the Bratteli diagrams. The simplest and most important class AF-algebras from this point of view is called "standard algebras" (standard filtrations).  The main definition came from egodic and measure theory, but also became important in topological category.

This theory applies to the theory of traces of algebras, and characters of the groups as well as the theory of invariant measures in dynamics.