| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Outline of Final Research Achievements |
We can interpret differential Galois theory as a theory of Module algebras under the Hopf algebra of the co-orrdinate ring of the 1 dimensional additive group. Hopf algebraists succeeded in generalizing the theory of linear equations from this view point, to a co-commutative Hopf algebra acting on a commutative module algebra. There arises a natural question whether we can extend this general theory to non-commutative case, or we can quantize it. Using the notion of Galois hull born in our study of Galois theory of non-linear differential equations, we successfully established a general Galois theory of non-commutative linear equations with constant coefficients.
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