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A classification is given of certain separable
nuclear C -algebras not necessarily of real rank
zero, namely, the class of simple C -algebras which
are inductive limits of continuous trace C -algebras
whose building blocks have spectrum homeomorphic to
the closed interval [0,1]. In particular, a
classification of simple stably AI algebras is
obtained. Also, the range of the invariant is calculated.
We start by approximating the building blocks
appearing in a given inductive limit decomposition by
certain special building blocks. The special building
blocks are continuous trace C -algebras with finite
dimensional irreducible representations and such that
the dimension of the representations, as a function
on the interval, is a finite (lower semicontinuous)
step function. It is then proved that these
C -algebras have finite presentations and stable
relations. The advantage of having inductive limits
of special subhomogeneous algebras is that we can
prove the existence of certain gaps for the induced
maps between the affine function spaces. These gaps
are necessary to prove the Existence Theorem. Also
the Uniqueness theorem is proved for these special
building blocks.
nuclear C -algebras not necessarily of real rank
zero, namely, the class of simple C -algebras which
are inductive limits of continuous trace C -algebras
whose building blocks have spectrum homeomorphic to
the closed interval [0,1]. In particular, a
classification of simple stably AI algebras is
obtained. Also, the range of the invariant is calculated.
We start by approximating the building blocks
appearing in a given inductive limit decomposition by
certain special building blocks. The special building
blocks are continuous trace C -algebras with finite
dimensional irreducible representations and such that
the dimension of the representations, as a function
on the interval, is a finite (lower semicontinuous)
step function. It is then proved that these
C -algebras have finite presentations and stable
relations. The advantage of having inductive limits
of special subhomogeneous algebras is that we can
prove the existence of certain gaps for the induced
maps between the affine function spaces. These gaps
are necessary to prove the Existence Theorem. Also
the Uniqueness theorem is proved for these special
building blocks.