2013 Fiscal Year Final Research Report
Study of group actions on operator algebras
| Project/Area Number |
22740099
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Chiba University |
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Principal Investigator |
MATUI HIROKI 千葉大学, 理学(系)研究科(研究院), 教授 (40345012)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 作用素環 |
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| Research Abstract |
I studied group actions on operator algebras and related topics. In particular, I focused on simple nuclear C*-algebras, which can be thought of as non-commutative topological spaces. First, various group actions on simple nuclear C*-algebras were classified up to cocycle conjugacy. For instance, uniqueness of actions of finitely generated free abelian groups on UHF algebras of infinite type was obtained. Secondly, it was proved that a large class of simple nuclear C*-algebras are classified by their K-groups. Also, I showed that topological full groups associated with minimal dynamical systems have various interesting properties.
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