Classification theory of C*-algebras over finite spaces

2016 Fiscal Year Final Research Report

• Project/Area Number: 24740109
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Keio University
• Principal Investigator: KATSURA Takeshi 慶應義塾大学, 理工学部(矢上), 准教授 (50513298)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 数学 / 関数解析 / 作用素環 / 分類

Outline of Final Research Achievements

In this research, we got not only various results on C*-algebras over finite spaces as expected, but also wide results on classification theory of C*-algebras. The results on C*-algebras over finite spaces include the one on K-theoretical invariants of Cuntz-Krieger algebras with the application to the conjecture of characterization of graph algebras, the complete solution to realization problem of K-theoretical invariants of non-simple graph algebras, and the result of determining which AF-algebras arise as non-simple graph algebras. The results on classification theory of C*-algebras include the ones on non-separable C*-algebras and on C*-algebras associated with discrete groups.

Free Research Field

作用素環