2021 Fiscal Year Research-status Report
Tilting theory of gentle algebras via surface combinatorics
| Project/Area Number |
19K23401
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| Research Institution | Nagoya University |
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Principal Investigator |
チャン アーロンケイヤム 名古屋大学, 高等研究院(多元), 特任助教 (50845039)
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| Project Period (FY) |
2019-08-30 – 2023-03-31
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| Keywords | gentle algebras / surface combinatorics / Calabi-Yau algebras |
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| Outline of Annual Research Achievements |
Over the past year I have a new publication and have two other papers submitted for review.
One of the two submitted paper is directly related to the current KAKENHI project. Namely, we achieved a major step in our research plan, which is to classify torsion classes of gentle algebras using surface combinatorics. The other two paper are related to cluster-tilting theory. The published paper studies the classification of representation-finite gendo-symmetric algebras, which contains some of the Brauer graph algebras - one of the subject of interest in our KAKENHI project. The other project shows that fractional-Calabi-Yau property of an algebra reflects periodicity of its trivial extension. This has potential applications to many algebras appear in, for example, algebraic geometry.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Article submitted in time as expected
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| Strategy for Future Research Activity |
I am now attempting to relate gentle algebras with non-orientable surfaces, on top of the known orientable case. And aim to use this to give a categorification of the coordinate ring of decorated Techmuller space of non-orientable surfaces, just like the classical case does.
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| Causes of Carryover |
Travel to Oberwolfach (Germany) meeting in February 2021, and any possible travel use for joint research projects.
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