Department Colloquium

Location: RI 209

Speaker: Douglas Farenick, University of Regina

Title:  C*-algebras and operator systems with the lifting property

Abstract:

A unital C*-algebra or operator system E has the lifting property if every unital completely positive (ucp) linear map into a quotient C*-algebra A/K lifts to a ucp map from E to A. Although the lifting property has been studied for fifty years, it was only this summer that the question of whether every 3-dimensional operator system has the lifting property was resolved, thereby settling the so-called Smith-Ward problem. In this audience-friendly lecture, I will review some of the seminal and recent results regarding the lifting property, and present some new examples of low-dimensional operator systems with or without the lifting property, based on joint work with Mitra Maleki, Sofia Medina Varela, and Sushil Singla, as well as work with Vern Paulsen.