2016 Fiscal Year Final Research Report
Categorification of cluster algebras by quivers with potential
| Project/Area Number |
26800008
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
DEMONET Laurent 名古屋大学, 多元数理科学研究科(国際), G30特任准教授 (70646124)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | representation theory / finite dim algebras / categorification / cluster algebras |
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| Outline of Final Research Achievements |
The main results achieved during this project are the following. I studied orders in categorification of cluster algebras. In three articles (two with X. Luo and one with O. Iyama), we investigated one the one hand categorification of combinatorial models (triangulations of polygons) and on the other hand categorification coming from Lie theory (partial flag varieties). An other project (with O. Iyama and G. Jasso) consisted to study support tau tilting modules and torsion classes in the case of algebras having finitely many of them. In particular, we reached nice geometric realizations and good characterizations of those algebras. Finally, I introduced by myself a new class of algebras (algebras of partial triangulations) containing Brauer graph algebras as well as Jacobian algebras of surfaces. Moreover, this class of algebras have important properties (it has finite rank, has an easy to understand tilting theory and is of tame representation type).
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| Free Research Field |
algebra
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