2000 Fiscal Year Final Research Report Summary
Unbounded operator algebras and the applications to the quantum physics
| Project/Area Number |
11640222
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | FUKUOKA UNIVERSITY |
|---|
Principal Investigator |
INOUE Atsushi Fukuoka Univ., Fac.Sci., Professor, 理学部, 教授 (50078557)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TANAKA Naoto Fukuoka Univ., Fac.Sci., Associate Professor, 理学部, 助教授 (00247222)
KUSANO Takashi Fukuoka Univ., Fac.Sci., Professor, 理学部, 教授 (70033868)
KUROSE Hideki Fukuoka Univ., Fac.Sci., Professor, 理学部, 教授 (00161795)
OGI Hidekazu Fukuoka Institute of Tech.Univ., Fac.Engin., Associate Professor, 工学部, 助教授 (30248471)
|
|---|
| Project Period (FY) |
1999 – 2000
|
| Keywords | O^*-algebras / partial O^*-algebras / weights / standard weights / unbounded Tomita-Takesaki theory / quantum groups / locally convex *-algebras |
|---|
| Research Abstract |
We have studied unbounded Tomita-Takesaki theory which plays an important role for the structure theory and for applications to the quantum physics in the studies of algebras of unbounded operators (O^*-algebras, partial O^*-algebras). Weights on (partial) O^*-algebras are important for the physical applications (for example, the BCS-models) and for the structure of (partial) O^*-algebras.
We have defined the notion of standard weights on (partial) O^*-algebras which is possible to develop the unbounded Tomita-Takesaki theory, and generalized the modular theory, Connes cocycle theorem and Randon-Nikodym theorem for von Neumann algebras to the case of (partial) O^*-algebras. We have tried to apply the existence of Haar measur in the locally compact quantum group.
Furthermore, we have investigated weights and unbounded C^*-algebras for the structure theory and the representation theory of (locally convex) *-algebras.
|
