Continuous fields of C*-algebras over finite dimensional spaces

By Marius Dadarlat. 2006

78 citations recorded by the source corpus.

Abstract Let X be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of C ( X ) -algebras by C ( X ) -subalgebras with controlled complexity. The following applications are given. All unital separable continuous fields of C*-algebras over X with fibers isomorphic to a fixed Cuntz algebra O n , n ∈ { 2 , 3 , … , ∞ } , are locally trivial. They are trivial if n = 2 or n = ∞ . For n ⩾ 3 finite, such a field is trivial if and only if ( n − 1 ) [ 1 A ] = 0 in K 0 ( A ) , where A is the C*-algebra of continuous sections of the field. We give a complete list of the Kirchberg algebras D satisfying the UCT and having finitely generated K-theory groups for which every unital separable continuous field over X with fibers isomorphic to D is automatically locally trivial or trivial. In a more general context, we show that a separable unital continuous field over X with fibers isomorphic to a KK-semiprojective Kirchberg C*-algebra is trivial if and only if it satisfies a K-theoretical Fell type condition.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66a980faca1eaa3110cee24be61648364b3cb999

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

On the KK-theory of strongly self-absorbing C*-algebras (2007, background): “1 was known before for D a UHF algebra of infinite type and X a CW complex by [13], for D = O2 by [8] and [10], and for D = O∞ by [2].”