On the classification of C*-algebras of real rank zero .2.

• 成果类型: Article
• 署名作者: Elliott, GA; Gong, GH
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2118565
• 发表日期: 1996
• 页码: 497-610
• 关键词: topological stable rank; inductive limits; cstar-algebras; star-algebras; reduction

摘要

A classification is given of what may turn out to be all separable nuclear simple C*-algebras of real rank zero and stable rank one. (These terms refer to density of the invertible elements in the sets of self-adjoint elements and all elements, respectively, after adjunction of a unit.) The C*-algebras considered are those that can be expressed as the inductive limit of a sequence of finite direct sums of homogeneous C*-algebras with spectrum 3-dimensional finite CW complexes. This classification is also extended to include certain nonsimple algebras. The invariant used is the abelian group K-* = K-0 + K-1, together with the distinguished subset arising from partial unitaries in the algebra, the graded dimension range. With the semigroup generated by the graded dimension range as positive cone, K-* is an ordered group with the Riesz decomposition property which, in a suitable sense (allowing torsion) is unperforated. In fact, K-* is an arbitrary (countable) graded ordered group with these two properties. (This extends the theorem of Effros, Handelman, and Shen.)