| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
While quantum mechanics has made visible the noncommutativity of physical quantity, problems concerning noncommutative infinite groups and measure theory, such as the Banach-Tarsky paradox, have been found. Von Neumann, who devised the theory of operator algebras aiming at providing a mathematical foundation for quantum mechanics, introduced a good property of groups, named amenability, which enables avoidance of the paradox. The theory of operator algebras was originally derived from functional analysis, but the dynamical systems such as ergodic theory, noncommutatively modified, join to it automorphic group and its normal subgroup, which originated in Galois theory. As a result, amenability has become better understood, as is deeply related to infinite dimensional operators that can be approximated by finite dimensional operators. This matter provides an interesting contribution to the philosophy of mathematics, which is related to the developement of concepts in the sciences.
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