2013 Fiscal Year Final Research Report
Study on locally compact quantum groups and measured groupoids
| Project/Area Number |
22540215
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tokyo Gakugei University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
AOI Hisashi 立命館大学, 理工学部, 准教授 (90396276)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 関数解析学 / 作用素環 / フォンノイマン環 / 局所コンパクト量子群 / 測度付き同値関係 / エルゴード性 / ヘッケ対 / ヘッケ環 |
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| Research Abstract |
In this research, I initiated a study on ergodic measured equivalence relations together with their sub relations, from the viewpoint that they are naturally regarded as a generalization of groups in algebra. During the research, I particularly focused on a pair of an equivalence relation and its sub relation that together form a ``Hecke pair", which is a notion introduced in my earlier research. The notion of ``Hecke pair" was originally developed and studied in number theory, so I started my research, hoping (conjecturing) that I might be able to build a similar theory in the framework of measured equivalence relations. As a result along this line of research, I was able to define and construct, from a Hecke pair of equivalence relations, an operator-algebraic version of a Hecke algebra. I was also able to clarify a relation between our theory and the notion of Schlichting completion. In this way, I obtained several results that seem to support the validity of my conjecture.
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