2002 Fiscal Year Final Research Report Summary
Research on quantum matrices and Hopf algebras
| Project/Area Number |
11640007
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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 |
MITSUSHIRO Takeuchi Inst. of Math. Prof., 数学系, 教授 (00015950)
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| Co-Investigator(Kenkyū-buntansha) |
NAITO Satoshi Inst. of Math. Ass. Prof, 数学系, 助教授 (60252160)
MORITA Jun Inst. of Math. Prof., 数学系, 教授 (20166416)
MIYAMOTO Masahiko Inst. of Math. Prof., 数学系, 教授 (30125356)
MASUDA Tetsuya Inst. of Math. Ass. Prof, 数学系, 助教授 (70202314)
MASUOKA Akira Inst. of Math. Ass. Prof, 数学系, 助教授 (50229366)
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| Project Period (FY) |
1999 – 2002
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| Keywords | quantum matrix / quantum group / Hopf algebra / braid / modular category / braided category / biFrobenius algebra / cylinder matrix |
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| Research Abstract |
The principal investigator has studied quantum matrices and Hopf algebras related to quantum groups and obtained the following results. 1.Results on finite Hopf algebras in braided categories including Hopf modules and integrals appear in J. Pure and Appl. Algebra. 2. New concepts of cylinder matrix and cylinder algebra are investigated as variation of quantum matrices and the results appear in J. Algebra. 3. New concept of biFrobenius algebra arises from a joint work with Doi and its basic properties and the braid version appear in Contemp. Math.. 4. Modular categories and Hopf algebras are studied from a new point of view and an elementary proof of Etingof and Gelaki's theorem on dimension of irreducible modules is obtained and appears in J. Algebra. 5. Survey on quantum matrices with emphasis on braid theory, quantized linear algebra, Homfly polynomial, Hecke algebra and q-Schur algebra, cocycle deformation appears in MSRI Publ.. 6. ESS-LYZ theory on matched pairs of groups is studied from a new point of view and some new results are obtained. 7. Radford-Majid bosonization is studied from a new point of view.
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