## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

**Returning to in-person experiences in February:** Visit the COVID-19 website for more information.

Friday, October 3, 2014 — 3:30 PM EDT

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.

Location

MC - Mathematics & Computer Building

5046

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.