2001 Fiscal Year Final Research Report Summary
Classification of Hopf algebras and quantum groups by tensor equivalences
| Project/Area Number |
12640008
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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, Inst.of Math., 数学系, 助教授 (50229366)
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| Co-Investigator(Kenkyū-buntansha) |
MASUDA Tetsuya University of Tsukuba, Inst.of Math., 数学系, 助教授 (70202314)
MORITA Jun University of Tsukuba, Inst.of Math., 数学系, 教授 (20166416)
TAKEUCHI Mitsuhiro University of Tsukuba, Inst.of Math., 数学系, 教授 (00015950)
TANABE Kenichiro University of Tsukuba, Inst.of Math., 数学系, 助手 (10334038)
FUJITA Hisamasa University of Tsukuba, Inst.of Math., 数学系, 講師 (60143161)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Hopf algebra / Quantum group / Tensor equivalence / Cocfuasi-bialgebra / Crossed product / Hopf cohomology / Hochschild cohomology |
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| Research Abstract |
Our new results are divided roughly into two. First, we have classified some range of coquasi-bialgebras, which generalize Hopf algebras, up to tensor equivalences of their comodule categories ; this was done by constructing related cohomology groups, in a very concrete way with use of braid diagrams. Second, we have obtained a new result on crossed products, and thereby proved in a unified way three famous theorems for affine group schemes ; this was based on the idea that the Hopf cohomology, which is non-abelian and multiplicative, can be approximated, in some sense, by the HochschiId cohomology, which is abelian and additive.
The results were annonced at the following conferences.
The 46-th Symposium on Algebra, Osaka Univ., July 30-August 2, 2001.
Non-commutative Geometry and Quantum Groups, Banach Center (Warsaw), September 17-29, 2001.
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Research Products
(9 results)
