2021/07/07 更新

写真a

チャン アーロン ケイ ヤム
CHAN Aaron Kay Yam
CHAN Aaron Kay Yam
所属
高等研究院 特任助教
大学院多元数理科学研究科 特任助教
職名
特任助教

学位 1

  1. Master in Mathematics ( 2010年7月   University of Cambridge (UK) ) 

研究キーワード 1

  1. representation theory; finite dimensional algebras

研究分野 2

  1. 自然科学一般 / 代数学  / Representation theory of finite dimensional algebras

  2. 自然科学一般 / 代数学

現在の研究課題とSDGs 2

  1. Representation theory of finite dimensional algebras

  2. 2-representation theory of finitary categories

経歴 3

  1. 名古屋大学   多元数理科学研究科   学振外国人特別研究員

    2017年4月 - 2019年3月

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    国名:日本国

  2. 名古屋大学   多元数理科学研究科   助教授

    2016年8月 - 2017年3月

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    国名:日本国

  3. Uppsala University   Department of Mathematics   Post-doctoral researcher

    2014年10月 - 2016年3月

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    国名:スウェーデン王国

学歴 2

  1. University of Aberdeen   Faculty of Science Department of Mathematics   Mathematical Science

    2010年9月 - 2014年7月

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    国名: グレートブリテン・北アイルランド連合王国(英国)

  2. University of Cambridge   Faculty of Mathematics   Mathematical Science

    2006年10月 - 2010年7月

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    国名: グレートブリテン・北アイルランド連合王国(英国)

 

論文 11

  1. Irreducible representations of the symmetric groups from slash homologies of p-complexes

    Aaron Chan

    Algebraic Combinatorics     2021年2月

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    掲載種別:研究論文(学術雑誌)  

  2. Irreducible representations of the symmetric groups from slash homologies of p-complexes 査読有り

    Chan A., Wong W.

    Algebraic Combinatorics   4 巻 ( 1 ) 頁: 125 - 144   2021年

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    記述言語:日本語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Algebraic Combinatorics  

    In the 40s, Mayer introduced a construction of (simplicial) p-complex by using the unsigned boundary map and taking coefficients of chains modulo p.We look at such a p-complex associated to an (n - 1)-simplex; in which case, this is also a p-complex of representations of the symmetric group of rank n - specifically, of permutation modules associated to two-row compositions. In this article, we calculate the so-called slash homology - a homology theory introduced by Khovanov and Qi - of such a p-complex. We show that every non-trivial slash homology group appears as an irreducible representation associated to two-row partitions, and how this calculation leads to a basis of these irreducible representations given by the so-called p-standard tableaux.

    DOI: 10.5802/ALCO.153

    Scopus

  3. On simple-minded systems and tau-periodic modules of self-injective algebras

    Chan Aaron, Liu Yuming, Zhang Zhen

    JOURNAL OF ALGEBRA   560 巻   頁: 416 - 441   2020年10月

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    記述言語:日本語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Journal of Algebra  

    Let A be a finite-dimensional self-injective algebra over an algebraically closed field, C a stably quasi-serial component (i.e. its stable part is a tube) of rank n of the Auslander-Reiten quiver of A, and S be a simple-minded system of the stable module category mod_A. We show that the intersection S∩C is of size strictly less than n, and consists only of modules with quasi-length strictly less than n. In particular, all modules in the homogeneous tubes of the Auslander-Reiten quiver of A cannot be in any simple-minded system.

    DOI: 10.1016/j.jalgebra.2020.05.024

    Web of Science

    Scopus

  4. COIDEMPOTENT SUBCOALGEBRAS AND SHORT EXACT SEQUENCES OF FINITARY 2-REPRESENTATIONS 査読有り 国際共著

    AARON CHAN, VANESSA MIEMIETZ

    Nagoya Mathematical Journal     頁: 1 - 26   2020年3月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Cambridge University Press ({CUP})  

    DOI: 10.1017/nmj.2020.1

  5. Auslander-Gorenstein algebras from Serre-formal algebras via replication 査読有り

    Chan Aaron, Iyama Osamu, Marczinzik Rene

    ADVANCES IN MATHEMATICS   345 巻   頁: 222 - 262   2019年3月

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    記述言語:日本語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Advances in Mathematics  

    We introduce a new family of algebras, called Serre-formal algebras. They are Iwanaga–Gorenstein algebras for which applying any power of the Serre functor on any indecomposable projective module, the result remains a stalk complex. Typical examples are given by (higher) hereditary algebras and self-injective algebras; it turns out that other interesting algebras such as (higher) canonical algebras are also Serre-formal. Starting from a Serre-formal algebra, we consider a series of algebras – called the replicated algebras – given by certain subquotients of its repetitive algebra. We calculate the self-injective dimension and dominant dimension of all such replicated algebras and determine which of them are minimal Auslander–Gorenstein, i.e. when the two dimensions are finite and equal to each other. In particular, we show that there exist infinitely many minimal Auslander–Gorenstein algebras in such a series if, and only if, the Serre-formal algebra is twisted fractionally Calabi–Yau. We apply these results to a construction of algebras from Yamagata [29], called SGC extensions, given by iteratively taking the endomorphism ring of the smallest generator-cogenerator. We give a sufficient condition so that the SGC extensions and replicated algebras coincide. Consequently, in such a case, we obtain explicit formulae for the self-injective dimension and dominant dimension of the SGC extension algebras.

    DOI: 10.1016/j.aim.2019.01.010

    Web of Science

    Scopus

  6. On Representation-Finite Gendo-Symmetric Biserial Algebras 査読有り

    Chan Aaron, Marczinzik Rene

    ALGEBRAS AND REPRESENTATION THEORY   22 巻 ( 1 ) 頁: 141 - 176   2019年2月

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    記述言語:日本語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Algebras and Representation Theory  

    Gendo-symmetric algebras were introduced by Fang and Koenig (Trans. Amer. Math. Soc., 7:5037–5055, 2016) as a generalisation of symmetric algebras. Namely, they are endomorphism rings of generators over a symmetric algebra. This article studies various algebraic and homological properties of representation-finite gendo-symmetric biserial algebras. We show that the associated symmetric algebras for these gendo-symmetric algebras are Brauer tree algebras, and classify the generators involved using Brauer tree combinatorics. We also study almost ν-stable derived equivalences, introduced in Hu and Xi (I. Nagoya Math. J., 200:107–152, 2010), between representation-finite gendo-symmetric biserial algebras. We classify these algebras up to almost ν-stable derived equivalence by showing that the representative of each equivalence class can be chosen as a Brauer star with some additional combinatorics. We also calculate the dominant, global, and Gorenstein dimensions of these algebras. In particular, we found that representation-finite gendo-symmetric biserial algebras are always Iwanaga-Gorenstein algebras.

    DOI: 10.1007/s10468-017-9760-6

    Web of Science

    Scopus

  7. Diagrams and discrete extensions for finitary 2-representations 査読有り

    Chan, A., Mazorchuk, V.

    Mathematical Proceedings of the Cambridge Philosophical Society   166 巻 ( 2 ) 頁: 325 - 352   2019年

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

    DOI: 10.1017/S0305004117000858

    Scopus

  8. Classification of two-term tilting complexes over Brauer graph algebras 査読有り

    Adachi Takahide, Aihara Takuma, Chan Aaron

    MATHEMATISCHE ZEITSCHRIFT   290 巻 ( 1-2 ) 頁: 1 - 36   2018年10月

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    記述言語:日本語   掲載種別:研究論文(学術雑誌)   出版者・発行元:Mathematische Zeitschrift  

    Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete.

    DOI: 10.1007/s00209-017-2006-9

    Web of Science

    Scopus

  9. Simple-minded systems, configurations and mutations for representation-finite self-injective algebras

    Aaron CHAN, Steffen KOENIG, Yuming LIU

    Journal of Pure and Applied Algebra   219 巻 ( 6 ) 頁: 1940-1961   2014年8月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

  10. Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras

    Aaron CHAN

    Algebra and Representation theory   18 巻 ( 1 ) 頁: 183-203   2014年6月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

  11. Some homological properties of tensor and wreath products of quasi-hereditary algebras

    Aaron CHAN

    Communication in Algebras   42 巻 ( 6 ) 頁: 2368-2379   2014年2月

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    記述言語:英語   掲載種別:研究論文(学術雑誌)  

▼全件表示

MISC 1

  1. A geometric model of Brauer graph algebras

    Takahide Adachi, Aaron Chan  

    Proceedings of the 51st Symposium on Ring Theory and Representation Theory   2019年2月

講演・口頭発表等 3

  1. Rings and representation theory

    Aaron CHAN

    49th Japan Ring Symposium 

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    開催年月日: 2016年8月 - 2016年9月

    記述言語:英語   会議種別:口頭発表(一般)  

    国名:日本国  

  2. Representation theory 国際会議

    Aaron CHAN

    Workshop on Brauer graph algebras 

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    開催年月日: 2016年3月

    記述言語:英語   会議種別:口頭発表(一般)  

    国名:ドイツ連邦共和国  

  3. Representation theory

    Aaron CHAN

    39th ARTIN meeting 

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    開催年月日: 2014年3月

    記述言語:英語   会議種別:口頭発表(一般)  

    国名:グレートブリテン・北アイルランド連合王国(英国)  

科研費 2

  1. Tilting theory of gentle algebras via surface combinatorics

    2019年10月 - 2020年10月

    Grant-in-Aid for Scientific Research 

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    担当区分:研究代表者 

  2. Tilting theory of gentle algebras via surface combinatorics

    研究課題/研究課題番号:19K23401  2019年8月 - 2021年3月

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity start-up  Grant-in-Aid for Research Activity start-up

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    担当区分:研究代表者 

    配分額:2860000円 ( 直接経費:2200000円 、 間接経費:660000円 )