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

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig [15,16] addressed some behaviour of the endomorphism algebra of a generator over a symmetric algebra, which they called gendo-symmetric algebra. Continuing this line of works, we classify in this article the representation-finite gendo-symmetric algebras that have precisely one isomorphism class of indecomposable non-injective projective module. We also determine their almost ν-stable derived equivalence classes in the sense of Wei Hu and Changchang Xi [21]. It turns out that a representative can be chosen as the quotient of a representation-finite symmetric algebra by the socle of a certain indecomposable projective module.

DOI： 10.1016/j.jalgebra.2022.04.002

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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：Nagoya Mathematical Journal  

In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra 1-morphism defining this middle term. We additionally relate these to recollements of the underlying abelian 2-representations.

DOI： 10.1017/nmj.2020.1

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掲載種別：研究論文（学術雑誌）  

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

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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

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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  

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  

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)