2022 Fiscal Year Annual Research 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 | Auslander correspondence / Koszul duality / Non-orientable surface / gentle algebras / categorification / cluster algebras |
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| Outline of Annual Research Achievements |
I have finished two preprints that are submitted and currently under review.
The first one is titled "Dominant Auslander-Gorenstein algebras and Koszul duality". This research studies a certain generalisation of Auslander algebra and extended the Auslander correspondence to a larger class of algebras. Moreover, we also showed that this class is closed under Koszul duality and looked at some interesting examples.
The second preprint is titled "Marked non-orientable surfaces and cluster categories via symmetric representations". We bring in new technology to extend the study of algebras associated to orientable surfaces to non-orientable ones. This research provide the first important step towards categorification of cluster algebra-like objects associated to non-orientable surfaces.
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