Noncommutative Geometry Seminar

Date: April 16, 2025

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Lara Ismert, University of Nebraska-Lincoln

Title: The infinite path space of a quantum graph

Abstract: In a 2022 article, Brannan, Eifler, Voigt, and Weber defined an equivalent notion of a quantum graph via a {\em quantum adjacency matrix} on a finite-dimensional {\em quantum set}. As a quantum analogue of a Schur idempotent matrix, a quantum graph’s quantum adjacency matrix serves as a jumping off point to generalize the Cuntz—Krieger algebra arising from a classical {0,1}-matrix. The four authors also introduced two quantum Cuntz—Krieger relations on a non-commutative finite-dimensional C*-algebra which generalize the respective Cuntz—Krieger relations defined on a commutative finite-dimensional C*-algebra.