Gauge Invariant Uniqueness Theorem for Corners of k-graphs
Abstract
Description
For a finitely aligned k-graph $Λ$ with X a set of vertices in $Λ$ we define a universal C*-algebra called $C^*(Λ,X)$ generated by partial isometries. We show that $C^*(Λ,X)$ is isomorphic to the corner $P_XC^*(Λ)P_X$, where $P_X$ is the sum of vertex projections in X. We then prove a version of the Gauge Invariant Uniqueness Theorem for $C^*(Λ,X)$, and then use the theorem to prove various results involving fullness, simplicity and Morita equivalence as well as new results involving symbolic dynamics.
12 pages, no figures
12 pages, no figures