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MORPHISMS OF SIMPLE TRACIALLY AF ALGEBRAS

MARIUS DADARLAT

Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

https://doi.org/10.1142/S0129167X04002636Cited by:13 (Source: Crossref)

Abstract

Let A, B be separable simple unital tracially AF C*-algebras. Assuming that A is exact and satisfies the Universal Coefficient Theorem (UCT) in KK-theory, we prove the existence, and uniqueness modulo approximately inner automorphisms, of nuclear *-homomorphisms from A to B with prescribed K-theory data. This implies the AF-embeddability of separable exact residually finite-dimensional C*-algebras satisfying the UCT and reproves Huaxin Lin's theorem on the classification of nuclear tracially AF C*-algebras.

Keywords:

AMSC: 46L35, 19K14, 19K35

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