Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
“K0 of a C*-algebra, continued”
For a C*-algebra A, we define an abelian group K0(A) by groupifying the monoid of Murray–von Neumann equivalence classes of projection matrices over A. We saw that K0(C) ≃ Z, and this time we will continue with more examples. Elliott’s Theorem essentially states that for two AF-algebras A, B, we have A ≃ B if and only if K0(A) ≃ K0(B), with the caveat that the isomorphism between K0 must preserve some additional structure. The aim is to outline what exactly that additional structure is.