Subalqebras of simple AF-alqebras

• 成果类型: Article
• 署名作者: Schafhauser, Christopher
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.192.2.1
• 发表日期: 2020
• 页码: 309-352
• 关键词: C-ASTERISK-ALGEBRAS; corona factorization property; baum-connes conjecture; crossed-products; star-algebras; UNITARY EQUIVALENCE; inductive limits; K-THEORY; CLASSIFICATION; rank

摘要

It is shown that if A is a separable, exact C*-algebra which satisfies the Universal Coefficient Theorem (UCT) and has a faithful, amenable trace, then A admits a trace-preserving embedding into a simple, unital AF algebra with a unique trace. Modulo the UCT, this provides an abstract characterization of C*-subalgebras of simple, unital AF-algebras. As a consequence, for a countable, discrete, amenable group G acting on a second countable, locally compact, Hausdorff space X, C-o(X) infinity(r) G embeds into a simple, unital AF-algebra if, and only if, X admits a faithful, invariant, Borel, probability measure. Also, for any countable, discrete, amenable group G, the reduced group C*-algebra C-r(*)(G) admits a trace-preserving embedding into the universal UHF-algebra.