Study of super-algebraic groups using Hopf algebras
| Project/Area Number |
26400035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
MASUOKA Akira 筑波大学, 数理物質系, 准教授 (50229366)
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| Research Collaborator |
SHIBATA Taiki 岡山理科大学, 理学部, 助教
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| 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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| Keywords | ホップ代数 / スーパー代数群 / テンソル圏 / ハリシュ-チャンドラ対 / 量子群 / 微・差分ガロア理論 / ピカール-ヴェシオ理論 / 淡中双対性 / スーパー・ハイパー代数 / ピカール・ヴェシオ理論 |
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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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Report
(4 results)
Research Products
(14 results)
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[Journal Article] Lifting via cocycle deformation2014
Author(s)
N. Andruskiewitsch, I. Angiono, A. Garcia Iglesias, 増岡 彰, C. Vay
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Journal Title
Journal of Pure and Applied Algebra
Volume: 218
Pages: 684-703
DOI
Related Report
Peer Reviewed / Open Access / Acknowledgement Compliant
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[Presentation] Hopf-algebraic approach to super affine groups2015
Author(s)
Akira Masuoka
Organizer
Workshop: Nichols Algebras and Their Interactions with Lie Theory, Hopf Algebras and Tensor Categories
Place of Presentation
Banff International Research Station (カナダ)
Year and Date
2015-09-09
Related Report
Int'l Joint Research / Invited
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