Hopf-Galois theoretic approach to quantum groups
Project/Area Number |
20540036
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
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Research Institution | University of Tsukuba |
Principal Investigator |
MASUOKA Akira University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (50229366)
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Project Period (FY) |
2008 – 2010
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Project Status |
Completed (Fiscal Year 2010)
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Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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Keywords | ホップ代数 / 量子群 / スーパー群スキーム / ピカール・ヴェシオ理論 / 量子包絡環 / 群スキーム / ホップガロア理論 / コサイクル変形 / ホップガロア拡大 / 量子ダブル / ピカール・ウェシオ理論 |
Research Abstract |
Hopf-Galois extensions of non-commutative algebras are a non-commutative analogue of principal homogeneous spaces(or torsors)in algebraic geometry, and of principal fiber bundles in algebraic topology. Ideas and techniques developed in Hopf-Galois theory can be effectively applied to study non-commutative or super-commutative algebras, and descent theory as well. The investigator did apply these to study quantum groups, algebraic super-groups and Picard-Vessiot theory. The obtained results include the construction of a series of Hopf algebras including the quantized enveloping algebras, by using cocycle deformation, together with its applications to study of generalized q-boson algebras and generalized quantum doubles.
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Report
(4 results)
Research Products
(21 results)
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[Journal Article]2009
Author(s)
天野勝利、増岡彰、竹内光弘
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Journal Title
Handbook of Algebra Vol.6(分担執筆Hopf algebraic Approach to Picard-Vessiot Theoryの章)(Elsevier/North-Holland)
Pages: 127-171
Related Report
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