2014 Fiscal Year Final Research Report
Combinatorics of finite-dimensional algebras and quantum symmetry
| Project/Area Number |
22540015
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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 | Meijo University (2012-2014)
Kyoto University (2010-2011) |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Keywords | 代数的組合せ論 / Hopf代数 / 鏡映群 / 旗多様体 / Lefschetz性 |
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| Outline of Final Research Achievements |
In this project, we have obtained the results mainly on the following two themes.
(1) We have given a description of the Schubert calculus and its generalizations in terms of noncommutative differential structures on the Weyl groups. The main topics are the K-ring of the flag variety and the homology of the affine Grassmannian. We have described them as subalgebras of the Nichols-Woronowicz algebras associated with the corresponding Weyl groups.
(2) We have obtained some results on the Lefschetz property of finite-dimensional Gorenstein algebras. We have determined the set of the Lefschetz elements of the coinvariant algebra of the finite Coxeter groups (except H_4). We have also introduced a new class of Gorenstein algebras defined by matroids and proved its Lefschetz property when the matroid corresponds to a geometric modular lattice.
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| Free Research Field |
代数学
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