| Budget Amount *help |
¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000)
Fiscal Year 2023: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2022: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2021: ¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2020: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Outline of Final Research Achievements |
Amanability and Kazhdan's peoprty are the two most important concepts in analytic group theory. In the joint work with Yuhei Suzuki, the PI has proved that the several notions of amenability for group actions on operator algebras that have been proposed are all equivalent and given applications of this result. The elementary matrix group EL_d(R) for a finitely generated ring R is the most prominent example of groups with Kazhdan's property. The PI generalizes this fact to a non-unital ring. It is well-known that every operator on (the l_2 space of) a uniformly locally finite metric space that is approximable by finite-propagation operators is quasi-local. Since introduced in 90s, it has been questioned whether the converse also holds true. The PI has answered this in negative by constructing counterexamples.
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