| Project/Area Number |
14540007
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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 Univ.Tsukuba, Inst.Math., Assoc.Prof., 数学系, 助教授 (50229366)
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| Co-Investigator(Kenkyū-buntansha) |
FUJITA Hisamasa Univ.Tsukuba, Inst.Math., Assoc.Prof., 数学系, 助教授 (60143161)
MORITA Jun Univ.Tsukuba, Inst.Math., Prof., 数学系, 教授 (20166416)
TAKEUCHI Mitsuhiro Univ.Tsukuba, Inst.Math., Prof., 数学系, 教授 (00015950)
TANABE Ken-ichiro Univ.Tsukuba, Inst.Math., Assistant, 数学系, 助手 (10334038)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Hopf algebra / super-Hopf algebra / super-affine group / group cohomology / II_1 subfactor / Picard-Vessiot theory / Tanaka duality / 淡中双対定理 / ホモロジー代数 / ホップ・ガロア拡大 / 部分因子環 / 群のコホモロジー |
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| Research Abstract |
In what is called "Algebraic Groups" some kinds of objects are involved. The most generalized are affine group (schemes), or representable group-functors on the category of commutative algebras, which are necessarily represented by commutative Hopf algebras. A linearly algebraic group is precisely the group of rational points in a field of such an affine group whose representative Hopf algebra is supposed to be finitely generated. By replacing linear algebraic groups with the generalized object, affine groups or Hopf algebras, we can often remove assumptions such as finite generation, zero characteristic or algebraic closedness. By extending to non-commutative Hopf algebras, we reach the notion of quantum groups. Our team has investigated affine groups, super-affine groups and Hopf-Galois extensions (or non-commutative principal homogeneous spaces) from the view-point of non-commutative algebra and geometry.
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