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Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet
Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet
Mathematics Faculty Research Publications
Suppose that A is a separable C*-algebra and that G∗ is a (graded) subgroup of the ℤ/2-graded group K∗(A). Then there is a natural short exact sequence
0 → G∗ → K∗(A) → K∗(A)/G∗ → 0.
In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as
0 → A ⊗ [cursive]K → Aƒ → SAt → 0
where K∗(At) is the torsion subgroup of …