## Dilian Yang, University of Windsor

### “Cycline subalgebras of k-graph C*-algebras”

Higher rank graphs (or k-graphs) are a higher dimensional generalization of directed graphs; directed graphs are naturally identified with 1-graphs. The graph C*-algebra of a k-graph is the universal C*-algebra among its all Cuntz-Krieger families. Its cycline algebra is the sub- C*-algebra generated by the standard generators with equivalent pairs, where the equivalence essentially comes from the periodicity of the underlying k-graph.

In this talk, we answer two questions on cycline algebras arising from the recent study of a generalized Cuntz-Krieger uniqueness theorem by Brown-Nagy-Reznikoff: On one hand, we prove that the cycline subalgebra is a MASA in the k-graph C*-algebra; on the other hand, we provide an example to show that, in general, there is no conditional expectation from the k-graph C*-algebra onto the cycline algebra. If times permits, a sufficient condition that guarantees the existence of such conditional expectations will be given.