2019 Fiscal Year Final Research Report
The study of permanent properties for inclusions of C*-algebras and its application to the complex system
| Project/Area Number |
17K05285
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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 |
Basic analysis
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | Rokhlin property / C*-index theory / Jaing-Su absorption / Sequentially split / Operator means / Operator monotone / Schmidt rank / Completely positive maps |
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| Outline of Final Research Achievements |
We extended the tracial Rokhlin property for inclusions A ⊂ B of unital C*-algebras in the sense of Osaka and Teruya to the tracially sequentially split *-homomorphism for a *-homomorphism from A to B by using the idea by Balak and Szabo in the joint work with Hyun Ho Lee, and cleared the heredity of basic permanent properties of B to A. In the case of inclusions of nonunital C*-algebras, we finished the study of the Rokhlin property with Tamotsu Teruya.
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| Free Research Field |
作用素環論・作用素論
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| Academic Significance and Societal Importance of the Research Achievements |
離散群ΓからC*-環Aへの作用αから生成されるC*-力学系C*(Γ, A,α) (=B)の構造解析をBからAへの非可換条件付き期待値を用いて解析をするという大坂-照屋のアイデアを拡張したBalack-Szaboのsequentially split *-homomorphismをさらに拡張したLee-大坂の手法は、今後様々なC*-力学系の解析に役立つと期待できる。
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