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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik The Universal Coefficient Theorem for C*-Algebras with Finite Complexity
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The Universal Coefficient Theorem for C*-Algebras with Finite Complexity
Rufus Willett, Guoliang Yu (Broschiert, Englisch)
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Beschreibung
A C*-algebra satisfies the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet if it is equivalent in Kasparov’s KK-theory to a commutative C*-algebra. This paper is motivated by the problem of establishing the range of validity of the UCT, and in particular, whether the UCT holds for all nuclear C*-algebras.
We introduce the idea of a C*-algebra that “decomposes” over a class 𝒞 of… C*-algebras. Roughly, this means that locally there are approximately central elements that approximately cut the C*-algebra into two C∗-subalgebras from 𝒞 that have well-behaved intersection. We show that if a C*-algebra decomposes over the class of nuclear, UCT C∗-algebras, then it satisfies the UCT. The argument is based on a Mayer–Vietoris principle in the framework of controlled KK-theory; the latter was introduced by the authors in an earlier work. Nuclearity is used via Kasparov’s Hilbert module version of Voiculescu’s theorem, and Haagerup’s theorem that nuclear C*-algebras are amenable.
We say that a C*-algebra has finite complexity if it is in the smallest class of C*-algebras containing the finitedimensional
C*-algebras, and closed under decomposability; our main result implies that all C*-algebras in this class satisfy the UCT. The class of C*-algebras with finite complexity is large, and comes with an ordinal-number invariant measuring the complexity level. We conjecture that a C*-algebra of finite nuclear dimension and real rank zero has finite complexity; this (and several other related conjectures) would imply the UCT for all separable nuclear C*-algebras. We also give new local formulations of the UCT, and some other necessary and sufficient conditions for the UCT to hold for all nuclear C*-algebras. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.02.2024
Sprache
Englisch
EAN
9783985470662
Herausgeber
EMS Press
Serien- oder Bandtitel
MEMOIRS OF THE EUROPEAN MATHEMATICAL SOCIETY
Sonderedition
Nein
Autor
Rufus Willett, Guoliang Yu
Seitenanzahl
100
Auflage
1
Einbandart
Broschiert
-.-
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