28 citations · 75 across the 15 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…