| Simple stably projectionless C*-algebras, which are inductive limits of certain specified non-unital algebras of matrix-valued functions over finitely many copies of the interval [0,1], are shown to be classified by their positive tracial cone together with the subset of traces with finite norm at most equal to one. This generalizes Razak's example of Elliott's conjecture on classifying stably projectionless C*-algebras, to the case of inductive limits of finite direct sums of Razak's building block algebras.; The main part of the present thesis is the determination of the range of the invariant; it is shown that any topological cone, with a base consisting of a metrizable Choquet simplex, arises as the invariant of a simple C*-algebra inductive limit of single Razak building block algebras. As a result, we conclude that the C*-algebra inductive limits of basis building block algebras exhaust the whole class of C*-algebra inductive limits considered in this thesis. |
