2010 Fiscal Year Final Research Report
A study on quantum groups and von Neumann algebras concerning dual actions
| Project/Area Number |
19740090
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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 | Yamanashi Eiwa College |
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Principal Investigator |
AOI Hisashi Yamanashi Eiwa College, 理工学部, 准教授 (90396276)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 1コサイクル / エルゴード理論 / 余作用 / 作用素環論 / 双対作用 / 同値関係 / 誘導作用 / 関数解析 |
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| Research Abstract |
We investigated actions on von Neumann algebra by their dual actions. In this study, we proved that, for any coaction of a locally compact group K on a properly infinite von Neumann algebra and a closed subgroup H of K, the action is cocycle conjugate to a coaction which comes from a coaction of H if and only if the dual action is induced by an action of H. By using the notion of commensurability of ergodic measured equivalence subrelations, we also generalized the notion of Hecke algebras to von Neumann algebras which come from measured equivalence relations.
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