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2022 Fiscal Year Annual Research Report

Tilting theory of gentle algebras via surface combinatorics

Research Project

Project/Area Number 19K23401
Research InstitutionNagoya University

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)

Project Period (FY) 2019-08-30 – 2023-03-31
KeywordsAuslander correspondence / Koszul duality / Non-orientable surface / gentle algebras / categorification / cluster algebras
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.

  • Research Products

    (4 results)

All 2022 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (2 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results) Remarks (1 results)

  • [Journal Article] On representation-finite gendo-symmetric algebras with only one non-injective projective module2022

    • Author(s)
      Aihara Takuma、Chan Aaron、Honma Takahiro
    • Journal Title

      Journal of Algebra

      Volume: 603 Pages: 61~88

    • DOI

      10.1016/j.jalgebra.2022.04.002

    • Peer Reviewed
  • [Presentation] Algebras associated to surface dissections and their tilting theory2022

    • Author(s)
      Aaron Chan
    • Organizer
      Mathematics Society of Japan, 2022 Autumn meeting, Special lecture in algebra
    • Invited
  • [Presentation] Towards additive categorification of cluster-like algebras associated to non-orientable surfaces2022

    • Author(s)
      Aaron Chan
    • Organizer
      Trends in Cluster Algebras 2022
    • Int'l Joint Research / Invited
  • [Remarks] 個人ページ

    • URL

      http://aaronkychan.github.io/maths.html

URL: 

Published: 2023-12-25  

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