کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6425378 | 1633803 | 2015 | 29 صفحه PDF | دانلود رایگان |
We construct a compactly generated and closed symmetric monoidal stable â-category NSpâ² and show that hNSpâ²op contains the suspension stable homotopy category of separable Câ-algebras ΣHoCâ constructed by Cuntz-Meyer-Rosenberg as a fully faithful triangulated subcategory. Then we construct two colocalizations of NSpâ², namely, NSpâ²[Kâ1] and NSpâ²[Zâ1], both of which are shown to be compactly generated and closed symmetric monoidal. We prove that Kasparov KK-category of separable Câ-algebras sits inside the homotopy category of KKâ:=NSpâ²[Kâ1]op as a fully faithful triangulated subcategory. Hence KKâ should be viewed as the stable â-categorical incarnation of Kasparov KK-category for arbitrary pointed noncommutative spaces (including nonseparable Câ-algebras). As an application we find that the bootstrap category in hNSpâ²[Kâ1] admits a completely algebraic description. We also construct a K-theoretic bootstrap category in hKKâ that extends the construction of the UCT class by Rosenberg-Schochet. Motivated by the algebraization problem we finally analyze a couple of equivalence relations on separable Câ-algebras that are introduced via the bootstrap categories in various colocalizations of NSpâ².
Journal: Advances in Mathematics - Volume 285, 5 November 2015, Pages 72-100