2013 Fiscal Year Final Research Report
Noncommutative Analytic Approach for Discrete Group Theory
| Project/Area Number |
23540233
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
OZAWA Narutaka 京都大学, 数理解析研究所, 教授 (60323466)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 作用素環 / 関数解析 / 離散群論 |
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| Research Abstract |
Theory of operator algebras is a branch in Analysis which deals with noncommutative phenomena. In this project, Ozawa applied theory of operator algebras and studied the functional analytic aspects of theory of discrete groups. As an application, he constructed the first example of an amenable but not nuclear operator algebra. Connes's Embedding Conjecture is currently the most important conjecture in theory of operator algebras. Ozawa has proved that this conjecture is equivalent to Tsirelson's Conjecture, which has been being studied in Quantum Information Theory. He also studied the noncommutative real algebraic geometric aspects of these conjectures.
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