collaborators

5 papers

math.CO2025

Finite type and completeness of -fans

Toshiya Yurikusa

We study the -fan associated with a skew-symmetrizable matrix in the sense of cluster algebras. We show that a skew-symmetrizable matrix is of finite type if and only if its …

math.RT2025

Stable Brauer-Thrall II' conjecture for finite-dimensional Jacobian algebras

Mohamad Haerizadeh, Toshiya Yurikusa

We prove that finite-dimensional Jacobian algebras associated with non-degenerate quivers with potentials satisfy the stable Brauer-Thrall II' conjecture. In particular, this impli…

math.RT2025

Finite-dimensional Jacobian algebras: Finiteness and tameness

Mohamad Haerizadeh, Toshiya Yurikusa

Finite-dimensional Jacobian algebras are studied from the perspective of representation types. We establish that (like other representation types) the notions of -finiteness and…

math.RT2024

Dimension vectors of -rigid modules and -vectors of cluster monomials from triangulated surfaces

Toshiya Yurikusa

For the cluster algebra associated with a triangulated surface, we give a characterization of the triangulated surface such that different non-initial cluster monomia…

math.CO2024

Denseness of -vector cones from weighted orbifolds

Toshiya Yurikusa

We study -vector cones in a cluster algebra defined from a weighted orbifold of rank introduced by Felikson, Shapiro and Tumarkin. We determine the closure of the union of t…