Alexandros Chatzinikolaou: [WS1] Morita equivalence for quantum graphs: Operator systems and homomorphisms.

Speaker
Alexandros Chatzinikolaou, University of Athens

Abstract
Quantum graphs (or noncommutative graphs) are a noncommutative generalisation of graphs and can be defined as operator systems that are bimodules over the commutant of a finite dimensional C*-algebra. Morita equivalence for operator systems was introduced by Eleftherakis-Kakariadis-Todorov via the notion of TRO-equivalence. We investigate Morita equivalence for quantum graphs and characterise TRO equivalence of the operator systems via the existence of appropriate co-homomorphisms between the quantum graphs. This generalises a result of Eleftherakis-Kakariadis-Todorov regarding TRO equivalence of graph operator systems. We apply these ideas to show invariance of certain noncommutative graph parameters under Morita equivalence. This talk is based on an ongoing work with G. Hoefer, N. Koutsonikos-Kouloumpis, and I.A. Paraskevas.