28 citations · 75 across the 15 of their papers we have counts for
15 papers
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 …
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 im…
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…
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…
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…
Denominator vectors and dimension vectors from triangulated surfaces
Toshiya Yurikusa
In a categorification of skew-symmetric cluster algebras, each cluster variable corresponds with an indecomposable module over the associated Jacobian algebra. Buan, Marsh and Reit…
Acyclic cluster algebras with dense -vector fans
Toshiya Yurikusa
The -vector fans play an important role in studying cluster algebras and silting theory. We survey cluster algebras with dense -vector fans and show that a connected acyclic…
Bongartz completion via -vectors
Peigen Cao, Yasuaki Gyoda, Toshiya Yurikusa
In the present paper, we first give a characterization for Bongartz completion in -tilting theory via -vectors. Motivated by this characterization, we give the definition of…
Tame algebras have dense -vector fans
Bernhard Keller, Pierre-Guy Plamondon, Toshiya Yurikusa
The -vector fan of a finite-dimensional algebra is a fan whose rays are the -vectors of its -term presilting objects. We prove that the -vect…
Complete gentle and special biserial algebras are -tame
Toshitaka Aoki, Toshiya Yurikusa
The -vectors of two-term presilting complexes are important invariants. We study a fan consisting of all -vector cones for a complete gentle algebra. We show that any complet…
Density of -vector cones from triangulated surfaces
Toshiya Yurikusa
We study -vector cones associated with clusters of cluster algebras defined from a marked surface of rank . We determine the closure of the union of -vector cones…
-matrices of cluster algebras from triangulated surfaces
Yasuaki Gyoda, Toshiya Yurikusa
For a given marked surface and a fixed tagged triangulation of , we show that each tagged triangulation of is uniquely determined by the intersectio…
Combinatorial cluster expansion formulas from triangulated surfaces
Toshiya Yurikusa
We give a cluster expansion formula for cluster algebras with principal coefficients defined from triangulated surfaces in terms of perfect matchings of angles. Our formula simplif…
Wide subcategories are semistable
Toshiya Yurikusa
For an arbitrary finite dimensional algebra , we prove that any wide subcategory of satisfying a certain finiteness condition is -semistable for some stabili…
Cluster expansion formulas in type A
Toshiya Yurikusa
The aim of this paper is to give analogs of the cluster expansion formula of Musiker and Schiffler for cluster algebras of type A with coefficients arising from boundary arcs of th…