On the interplay between C^*-algebras and topological dynamical systems
| Project/Area Number |
09640226
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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 |
解析学
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| Research Institution | Japan Women's University |
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Principal Investigator |
TOMIYAMA Jun Japan Women's Univ., Fac.of Sci., Professor, 理学部, 教授 (30006928)
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| Co-Investigator(Kenkyū-buntansha) |
MINEMURA Katsuhiro Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (20060684)
FUJISAKI Rieko Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (30060635)
OEDA Kazuo Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (10060675)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1997: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | C^*-algebra / Topological dynamical system / Elementary sets of dynamical system / Orbit equivalence / Heat convection equation / Foliation / C^*-環 / C^* 環 / 充足群 |
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| Research Abstract |
The followings are main points of our results during the academic years through 1997 to 1998(Heisei 9-10). Among them, the first four items are carried out by Tomiyama.
1.Proved the restricted isomorphism theorem for the best possible wide classes of dynamical systems ; namely obtained the condition between dynamical systems when their associated C-algebras are isomorphic keeping the subalgebras of continuous functions for such a class.
2.Introduced the representation theory of dynamical systems as a new stand pointof the theory As consequences, we have reinforced the previous results in this field.
3.Cultivated various kinds of ways to attack the general isomorphism problem, among which one is the idea of universal C-Z-crossed product with its analysis andthe other is to distinguish the ideal of homeomorphism C-algebras as good and bad (and most bad) ones together with the characterizations of good ideals. Also analysed the properties of isomophisms from this point.
4.Obtained the C-algebraic descriptions of the behavior of nonwandering sets ofdynamical systems, the depths of the Birkhoff center. Among those elementary sets of dynamical systems, only this thing had been remained unsolved for several years.
5.Qeda has obtained the global solutions for the initial value problem of the heat convection equation in an exterior domain in the 2 or 3 dimensional Eucidean spaces. For a codimension q Hausdorff foliation having Torus as general leaves in the 4 or 5 dimensional compact manifold, Fujisaki has classified the types of singular leaves with the analysis of their local stabilities.
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Report
(3 results)
Research Products
(17 results)
