Functional analytic study on infinite dimensional groups
Project/Area Number |
26800055
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Shinshu University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2018-03-31
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Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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Keywords | 無限次元群 / ユニタリ群 / 自己共役作用素 / 同値関係 / 記述集合論 / Weyl-von Neumann同値 / von Neumann環 / ハイパー群 / ワイル・フォンノイマン同値関係 / 非有界作用素 / Hilbert空間 |
Outline of Final Research Achievements |
(1) We studied the unitary equivalence relation modulo the compacts for self-adjoint operators from a descriptive set theoretical point of view. It was shown that this equivalence relation cannot be classified by countable structures. (2) We studied topological groups which can be embedded into the unitary group of a finite von Neumann algebra. Such groups are called finite type groups. Finite type groups admit a compatible bi-invariant metric and can be embedded into the unitary group on a Hilbert space. It was shown that these two conditions are not sufficient to be a finite type group.
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Report
(5 results)
Research Products
(16 results)
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[Journal Article] Non-commutative hypergroup of order five2017
Author(s)
Yasumichi Matsuzawa, Hiromichi Ohno, Akito Suzuki, Tatsuya Tsurii, Satoe Yamanaka
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Journal Title
Journal of Algebra and Applications
Volume: 印刷中
Issue: 07
Pages: 1750127-1750127
DOI
NAID
Related Report
Peer Reviewed / Acknowledgement Compliant
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[Presentation] 無限次元群の話2015
Author(s)
松澤泰道
Organizer
作用素論作用素環論研究集会
Place of Presentation
KKR妙高高原白樺荘(新潟県妙高市)
Year and Date
2015-10-25
Related Report
Invited
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