Group Actions, Labelled Graphs, and C* -Algebras
Listen now
Description
This presentation does not require previous knowledge of C*-algebras, labeled graphs, or group actions. A labeled graph over an alphabet consists of a directed graph together with a labeling map . One can associate a C*-algebra to a labeled graph in such a way that if the labeling is trivial then the resulting C*-algebra is the C*-algebra of the graph . In this presentation, I will discuss joint work with Teresa Bates and David Pask concerning (discrete) group actions on labeled graphs and the resulting crossed product C*-algebras. In particular, I will discuss our main theorem which shows that the crossed product that arises when a group acts freely on a labeled graph is strongly Morita equivalent to the C*-algebra of the quotient graph of the action. I will focus on the two major ideas needed to prove this Morita equivalence. The first is a generalization of the so-called Gross-Tucker theorem, which shows that a free labeled graph action is naturally equivariantly isomorphic to a skew product action obtained from the quotient labeled graph. The second is a generalization of a theorem of Kaliszewski, Quigg, and Raeburn to the e ect that the C*-algebra of a skew product labeled graph is naturally isomorphic to a co-crossed product of a coaction of the group on the C*-algebra of the labeled graph.
More Episodes
Algebraic statistics advocates polynomial algebra as a tool for addressing problems in statistics and its applications. This connection is based on the fact that most statistical models are defined either parametrically or implicitly via polynomial equations. The idea is summarized by the phrase...
Published 04/28/11
Mathematical concepts are often difficult for students to acquire. This difficulty is evidenced by failure of knowledge to transfer from the learning situation to a novel isomorphic situation. What choice of instantiation most effectively facilitates successful transfer? One possibility is that...
Published 04/27/11
Current community models in the geosciences employ a variety of numerical methods from finite-difference, finite-volume, finite- or spectral elements, to pseudospectral methods. All have specialized strengths but also serious weaknesses. The first three methods are generally considered low-order...
Published 04/07/11