2010 Fiscal Year Final Research Report
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 |
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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 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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| 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 |
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| 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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