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Universal coefficient theorems for the stable Ext-groups. (English) Zbl 1194.46103
Summary: Let \(A\) be a unital separable nuclear \(C^{*}\)-algebra and let \(B\) be a stable \(C^{*}\)-algebra. Using \(K\)-theory and \(KK\)-theory, we establish universal coefficient theorems for the stable Ext-groups of unital extensions of \(A\) by \(B\) when \(A\) and \(B\) have certain properties, which generalize a result of L. Brown and M. Dadarlat for the strong Ext-groups. The class of extensions being studied are also enlarged.

MSC:
46L80 \(K\)-theory and operator algebras (including cyclic theory)
46L35 Classifications of \(C^*\)-algebras
19K33 Ext and \(K\)-homology
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