GEOMETRIC REALIZATION AND K-THEORETIC DECOMPOSITION OF C*-ALGEBRAS
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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 [Formula: see text] In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. We KK-theoretically decompose A as [Formula: see text] where K*(At) is the torsion subgroup of K*(A) and K*(Af) is its torsionfree quotient. Then we further decompose At: it is KK-equivalent to ⊕p Ap where K*(Ap) is the p-primary subgroup of the torsion subgroup of K*(A). We then apply this realization to study the Kasparov group K*(A) and related objects.
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1986 ◽
Vol 29
(1)
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pp. 97-100
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1997 ◽
Vol 08
(03)
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pp. 357-374
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2008 ◽
Vol 19
(01)
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pp. 47-70
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2017 ◽
Vol 69
(3)
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pp. 548-578
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2017 ◽
Vol 60
(1)
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pp. 77-94
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