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Nonstable K-theory for Z-stable C*-algebras

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arxiv math/9707228 v1 pith:MYOT7P63 submitted 1997-07-01 math.OA

Xinhui Jiang (Fields Institute) This is my paper · ORCID
classification math.OA
keywords algebrasfullprojectionsz-stablealgebraanalogouscancellationcomparability
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Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants, namely, \pi_i(U(A)) = K_{i-1}(A) for all integers i >= 0. Furthermore, A has cancellation for full projections, and satisfies the comparability question for full projections. Analogous results hold for non-unital Z-stable C^*-algebras.

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