9 citations · 25 across the 15 of their papers we have counts for
16 papers
Fans and polytopes in tilting theory III: Classification of convex -fans of rank 3
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
The -fan of a finite dimensional algebra is a non-singular fan in its real Grothendieck group, defined by tilting theory. If the union of the simplices a…
Frobenius--Perron dimension via -tilting theory
Takahide Adachi, Ryoichi Kase
From the perspective of -tilting theory, we study Frobenius--Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius--Perron dimensions of -tilting…
Fans and polytopes in tilting theory II: -fans of rank 2
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
The -fan of a finite dimensional algebra is a fan in its real Grothendieck group defined by tilting theory. We give a classification of complete -fans of rank 2. More explici…
Fans and polytopes in tilting theory I: Foundations
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
For a finite dimensional algebra over a field , the 2-term silting complexes of gives a simplicial complex called the -simplicial complex. We give tilting theo…
Examples of tilting-discrete self-injective algebras which are not silting-discrete
Takahide Adachi, Ryoichi Kase
In this paper, we introduce the notion of -stable silting-discrete algebras, which unify silting-discrete algebras and tilting-discrete self-injective algebras, where is a t…
Lengths of maximal green sequences for tame path algebras
Ryoichi Kase, Ken Nakashima
In this paper, we study the maximal length of maximal green sequences for quivers of type and by using the theory of tilting mutat…
From support -tilting posets to algebras
Ryoichi Kase
The aim of this paper is to study a poset isomorphism between two support -tilting posets. We take several algebraic information from combinatorial properties of support -til…
Self-injective cellular algebras of polynomial growth representation type
Susumu Ariki, Ryoichi Kase, Kengo Miyamoto +1
We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the base field has an odd…
Algebras sharing the same support -tilting poset with tree quiver algebras
Takuma Aihara, Ryoichi Kase
Happel and Unger reconstructed hereditary algebras from their posets of tilting modules. Inspired by this result, we try removing the assumption to be hereditary. However, it would…
Weak orders on symmetric groups and posets of support -tilting modules
Ryoichi Kase
We give a necessary and sufficient condition for that the support -tilting poset of a finite dimensional algebra is isomorphic to the poset of symmetric group with weak order. M…
Remarks on lengths of maximal green sequences for quivers of type
Ryoichi Kase
A maximal green sequence introduced by B. Keller is a certain sequence of quiver mutations at green vertices. T. Brüstle, G. Dupont and M. Pérotin showed that for an acyclic quive…
On components of stable Auslander-Reiten quivers that contain Heller lattices: the case of truncated polynomial rings
Susumu Ariki, Ryoichi Kase, Kengo Miyamoto
Let be a truncated polynomial ring over a complete discrete valuation ring , and we consider the additive category consisting of -lattices with the property…
Taking tilting modules from the poset of support tilting modules
Ryoichi Kase
C. Ingalls and H. Thomas defined support tilting modules for path algebras. From tau-tilting theory introduced by T. Adachi, O. Iyama and I. Reiten, a partial order on the set of b…
Distributive lattices and the poset of pre-projective tilting modules
Ryoichi Kase
D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. We…
A pre-projective part of tilting quivers of certain path algebras
Ryoichi Kase
D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. Fir…
The number of arrows in the quiver of tilting modules over a path algebra of type and
Ryoichi Kase
Happel and Unger defined a partial order on the set of basic tilting modules. The tilting quiver is the Hasse diagram of the poset of basic tilting modules. We determine the number…