$\mathbb Z^{k-1}$-Cartan subalgebras in $k$-graph $C^*$-algebras
Speaker:
Elizabeth Gillaspy, University of Montana
Date and Time:
Wednesday, November 8, 2023 - 11:00am to 11:30am
Location:
Online
Abstract:
Higher-rank graphs, or $k$-graphs, are $k$-dimensional generalizations of directed graphs; the combinatorial structure of the $k$-graph is reflected in the associated $C^*$-algebra. The first investigations of $k$-graph $C^*$-algebras, by Kumjian and Pask, showed that these C*-algebras have a canonical groupoid model. In joint work with J.H. Brown, we identify another groupoid model for certain $k$-graph $C^*$-algebras, using the concept of $\Gamma$-Cartan subalgebras introduced by Brown, Fuller, Pitts, and Reznikoff.