Yuta Kimura

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math.RT2026

Cohen-Macaulay representations of Artin-Schelter Gorenstein algebras of dimension one

Osamu Iyama, Yuta Kimura, Kenta Ueyama

Tilting theory is one of the central tools in modern representation theory, in particular in the study of Cohen-Macaulay representations. We study Cohen-Macaulay representations of…

math.RT2025

Tilting theoretic approach to quasi-hereditary structures

Takahide Adachi, Aaron Chan, Yuta Kimura +1

A quasi-hereditary algebra is an algebra equipped with a certain partial order $⊴$ on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives…

math.RT2025

Torsion classes of extended Dynkin quivers over commutative rings

Osamu Iyama, Yuta Kimura

For a Noetherian $R$ -algebra $I^$ , there is a canonical inclusion $tors I^ \to \prod_{p \in Spec R} tors (I^º (p) I^)$ , and each element in…

math.RT2025

Schur roots and tilting modules of acyclic quivers over commutative rings

Osamu Iyama, Yuta Kimura

Let $Q$ be a finite acyclic quiver and $A_{Q}$ the cluster algebra of $Q$ . It is well-known that for each field $k$ , the additive equivalence classes of support tilting $k Q$ -modules…