2010 Fiscal Year Final Research Report
Relative entropy for pairs of subalgebras and invariants arising from automorphisms
| Project/Area Number |
20540209
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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, 名誉教授 (80030378)
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| Co-Investigator(Kenkyū-buntansha) |
OKAYASU Rui 大阪教育大学, 教育学部, 准教授 (70362746)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 作用素環 / 非可換エントロピー / 自己同型写像 |
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| Research Abstract |
For a pair {A, B} of subalgebra of an operator algebra M, by modifying the Connes-Stormer relative entropy H(A|B), we defined h(A|B), and measured of distance between two algebras. For examples, in the case where M is the matrix algebra with the size n, then { h(A,B) ; A and B are maximal abelian subalgebras M}=[0.log n] and h(A,B)=log n iff A and B are mutually orthogonal. Similar result holds for pairs of subfactor with index 2 of type II_1 factors.
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