2004 Fiscal Year Final Research Report Summary
Entropy on non-commutative dynamical systems and the structure of operator algebras
| Project/Area Number |
14540205
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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 | Osaka Kyoiku University |
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Principal Investigator |
CHODA Marie Osaka Kyoiku University, Faculty of Education, (Mathematics), Professor, 教育学部, 教授 (80030378)
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| Co-Investigator(Kenkyū-buntansha) |
KATAYAMA Yoshikazu Osaka Kyoiku University, Faculty of Education, (Mathematics), Professor, 教育学部, 教授 (10093395)
FUJII Masatoshi Osaka Kyoiku University, Faculty of Education, (Mathematics), Professor, 教育学部, 教授 (10030462)
NAKAI Eiichi Osaka Kyoiku University, Faculty of Education, (Mathematics), Ass.Professor, 教育学部, 助教授 (60259900)
SADASUE Gaku Osaka kyoiku University, Faculty of Education, (Mathematics), Lecturer, 教育学部, 講師 (40324884)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Operator Algebars / Automorphism / Non-commutative dynamical system / Entropy / Group / State / Crossed product / free product |
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| Research Abstract |
1)An entropical invariant is defined for automorphisms of countable discrete amenable groups, and it is shown relations between two entropies for an automorphism on the C^*-crossed product algebra and for its restriction to the original algebra.
As an application to the free product^*, the topological entropy ht(θ) of an automorphism θ satishies that ht(θ^*θ^*......^*θ) = ht(θ^*1).
2)We showed that the free group factor L(Fm) has a continuous family of non conjugate outer actions of GL(n, Z) for all m=2, 3,..., and give an estimation of the Connes-Stormer entropy for each automorphism appearing in the actions.
By restrictng them to subgroups with Kazhdan's property T (for an example SL(n, Z), we have a continuous family of non cocycle conjugate outer actions on L(Fm), m>1.
3)Let G be a discrete subgroup of the automorphism group of an operator algebra A. Assume that G is exact, that is, it admits an amenable action on some compact space.
Then the entropy of an automorphism of the algebra A does not change by the canonical extension to the crossed product of A by G.
This is shown for the topological entropy of an exact C^* algebra A and for the dynamical entropy of an AFD von Neumann algebra A.
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Research Products
(16 results)
