2001 Fiscal Year Final Research Report Summary
Classification of automorphisms of C^*-algebras
| Project/Area Number |
10640197
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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 | HOKKAIDO UNIVERSITY |
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Principal Investigator |
KISHIMOTO Akitaka Hokkaido Univ., Grad. School of Science, Prof., 大学院・理学研究科, 教授 (00128597)
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| Project Period (FY) |
1998 – 2001
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| Keywords | Rohlin property / Extension / Pure state / Derivation / One-parameter automorphism group / Flow / Cuntz algebras / UHF algebras |
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| Research Abstract |
A classification result was obtained for outer classes of automorphisms of simple AT algebras of real rank zero in terms of KK theory. In doing so we introduced a new notion of ordered extension incorporating an order structure to the usual extensions, which is a new feature that does not show up in the case of purely infinite C^*-algebras.
Also a classification result was obtained for trace-scaling autmorphisms of certain AF algebras. This is an extension of similar results previously obtained by the head investigator et al.
The Rohlin property was shown for some specific automorphisms, which are far from approximately inner but trace-preserving. Thus this is an example which is not covered by the above-mentioned results.
Some novel examples were given to one-parameter automorphism groups of UHF algebras and AF algebras. This solves some old problems which have been resisting a solution for some time and opens up a new prospect to this old field.
The homogeneity was shown for the pure state space of a separable simple C^*-algebra under the action of automorphisms (or asymptotically inner automorphisms). This also solves an old problem and reveals an inner structure of such a C^*-algebra.
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