Finite-dimensional approximations and C*-algebraic K-theory
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2025
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Abstract
There are numerous ways in whiC*-algebras, this inC*-algebras, whiC*-algebra in half until ending up with something finite-dimensional. We relate this to other notions suC*-algebras. We show that torsion in the K1 group of a C*-algebra is an obstruction complexity rank one. Using the Kirchberg–Phillips classification theorem to compute the complexity rank of UCT Kirchberg algebras, we show that complexity rank equals one when the K1-group is torsion-free, and equals two otherwise.
Finally, using the Milnor exact sequence given by the controlled picture of KK-theory by Willett and Yu, we describe some topological properties of the topological group KK(A,B) with respect to the satisfaction of Mittag-Leffler and stability conditions of certain inverse systems.
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MathematiC*-algebras, K-theory, Topology
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106 pages
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