| 研究実績の概要 |
With Demonet, we classify all torsion classes of (possibly infinite dimensional and possibly global dimension infinite) gentle algebras. Our classification is to employ simple curves and laminations on compact oriented real-two-dimensional surfaces; such work is potentially useful in other areas such as topological Fukaya categories where gentle algebras are of central importance.
With Adachi, we study complexes of Brauer graph algebras. We employ topological techniques similar to results of Khovanov-Seidel to construct pretilting complexes of these algebras. We also calculate their endomorphism rings, and investigate the possiblity of them being tilting.
With Iyama and Marczinzik, we study generalisation of precluster tilting theory and minimal Auslander-Gorenstein. In particular, our results unify a previous work with Marczinzik on the study of special biserial gendo-symmetric algebras.
With Miemietz, we study the notion of short exact sequences for 2-representations of fiat 2-categories. We relate these notions with recollement of abelian categories, and found appropriate generalisation of localisation theory for coalgebras over a field to coalgebras objects arising in fiat 2-categories; this theory is applicable to setting of interests in other fields such as the study of module-category of a monoidal category.
With Wong, we study p-complexes of permutation modules in the setting of modular representations over the symmetric groups. We investigate the slash homologies of these complexes; in particular, we prove an extension of a conjecture of Wildon.
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