Completeness of the isomorphism problem for separable C*-algebras

被引：14
|
作者：
Sabok, Marcin [1 ,2 ]
机构：
[1] McGill Univ, Dept Math & Stat, 805 Sherbrooke St W, Montreal, PQ H3A 0B9, Canada
[2] Polskiej Akad Nauk, Inst Matemat, Ul Sniadeckich 8, PL-00956 Warsaw, Poland
来源：
INVENTIONES MATHEMATICAE | 2016年 / 204卷 / 03期
关键词：
FREE ABELIAN-GROUPS; CLASSIFICATION PROBLEM; BANACH-SPACES; INDUCTIVE LIMITS; COMPLEXITY; FINITE; HOMOMORPHISMS; ISOMETRY;
D O I：
10.1007/s00222-015-0625-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
引用
收藏
页码：833 / 868
页数：36
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