Completeness of the isomorphism problem for separable C*-algebras

• 成果类型: Article
• 署名作者: Sabok, Marcin
• 署名单位: McGill University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0625-5
• 发表日期: 2016
• 页码: 833-868
• 关键词: free abelian-groups; classification problem; banach-spaces; inductive limits; complexity; Finite; homomorphisms; isometry

摘要

This paper studies the descriptive set-theoretical complexity of the isomorphism problem for separable C*-algebras. We prove that the isomorphism problem for separable (simple, AI) C*-algebras is complete in the class of orbit equivalence relations. This means that any isomorphism problem arising from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple, separable AI C*-algebras.