2002 Fiscal Year Final Research Report Summary
Systematic study of quantum groups from the viewpoint of operator algebras
| Project/Area Number |
12640199
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | HOKKAIDO UNIVERSITY |
|---|
Principal Investigator |
YAMANOUCHI Takehiko Hokkaido University, Department of Mathematics ; Assistant Professor, 大学院・理学研究科, 助教授 (30241293)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
UEDA Yoshimichi Kyushu University, Graduate School of Mathematics ; Assistant Professor, 数理学研究院, 助教授 (00314724)
ARAI Asao Hokkaido University, Department of Mathematics ; Professor, 大学院・理学研究科, 教授 (80134807)
KISHIMOTO Akitaka Hokkaido University, Department of Mathematics ; Professor, 大学院・理学研究科, 教授 (00128597)
|
|---|
| Project Period (FY) |
2000 – 2002
|
| Keywords | Locally compact quantum group / von Neumann algebra / Cartan subalgebra / Galois group / Nontype I C^*-algebra / Approximately inner automorphism / Amalgamated free product / Jones index |
|---|
| Research Abstract |
Yamanouchi has made an intensive study of actions of locally compact quantum groups on von Neumann algebras. He introduced a notion of a Galois group for such an action. He has succeeded in topologically identifying the Galois group of an intergrable, minimal action of a general locally compact quantum group as the intrinsic group of the dual quantum group.
Kishimoto has made a very unique research on automorphisms or one-parameter automorphism groups on nontype I separable C^*-algebras. He showed that, for any irreducible representation of such a C^*-algebra without nonzero intersection with compact operators, there exists an approximately inner one-parameter automorphism group so that the representation is covariant with respect to this one-parameter automorphism group.
Arai has made a progress in his research in mathematical physics. He considered a model of quantum particles coupled to a massless quantum scalar field, and showed that the model has a ground state for all values of the coupling constant.
Ueda has made an anlysis on amalgamated free products of von Neumann algebras over Cartan subalgebras. By utilizing an irreducible inclusion of type III factors coming from his free-product type action of the quantum SU_q(2), he has been ble to solve the long-standing problem that the free group factor of Radulescu possesses irreducible subfactors of arbitrary index greater than 4.
|
Research Products
(13 results)
