Analysis Seminar: Domains of Quantum Metrics on AF algebras (Katrine von Bornemann Hjelmborg, University of Southern Denmark (SDU))

Title: Domains of Quantum Metrics on AF algebras

Abstract: Given a compact quantum metric space (A, L), we prove that the domain of L coincides with A if and only if A is finite-dimensional. Intuitively, this should allow for different quantum metrics with distinct domains when A is infinite-dimensional, and we show how to explicitly build such quantum metrics. Lastly, we also provide a strategy for the calculation of distance between certain states in these quantum metrics in the special cases of the quantized interval and the Cantor space. This is joint work with Konrad Aguilar and Frédéric Latrémolière.