Algebry operatorów i ich zastosowania w fizyce

It's well known that *-homomorphisms from a finite injective von Neumann algebra into the ultrapower of the hyperfinite II_1 factor are classified up to unitary equivalence by their behaviour on traces. At the level of C*-algebras there are annoying K-theoretic obstructions to analogous classification results. In this talk, I'll discuss how we can circumvent these obstructions by working with coloured equivalence, and discuss some applications of this result.