| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
The notion of algebraic groups is generalized by that of algebraic super-groups. This generalization is important, because every rigid abelian symmetric tensor category over an algebraically closed field of characteristic zero is realized as the category of finite-dimensional representations of some algebraic super-group, as was proved by P. Deligne. The project aims at characteristic-free study of algebraic super-groups using Hopf-algebraic methods and techniques. A category equivalence between algebraic super-groups defined over a commutative ring and Harish-Chandra pairs is proved. The result is applied to re-construct the so-called Chevalley super-groups over the ring of integers. For algebraic super-groups over a field, the properties, such as (i) solvability, (ii) nilpotency and (ii) the Chevalley-type decomposition, are investigated. The results will be hopefully applied to establish a super-analogue of the generalized Picard-Vessiot Theory produced by the PI and K. Amano.
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