30 citations · 81 across the 19 of their papers we have counts for
20 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…
-tilting theory and silting theory of skew group algebra extensions
Yuta Kimura, Ryotaro Koshio, Yuta Kozakai +2
Let be a finite dimensional algebra with an action by a finite group and the skew group algebra. One of our main results asserts that the canonical restriction-in…
Derived preprojective algebras and spherical twist functors
Yuya Mizuno, Dong Yang
We study silting objects over derived preprojective algebras of acyclic quivers by giving a direct relationship between silting objects, spherical twist functors and mutations. Esp…
Dimensions of -tilting modules over path algebras and preprojective algebras of Dynkin type
Toshitaka Aoki, Yuya Mizuno
In this paper, we introduce a new generating function called -polynomial for the dimensions of -tilting modules over a given finite dimensional algebra. Firstly, we study bas…
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…
Shard theory for -fans
Yuya Mizuno
For a finite dimensional algebra , the notion of -fan is defined from two-term silting complexes of in the real Grothendieck group $K_0(\mathsf{proj} A)_{\mathbb{R…
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…
Arc diagrams and 2-term simple-minded collections of preprojective algebras of type
Yuya Mizuno
We study an explicit description of semibricks and 2-term simple-minded collections over preprojective algebras of type via arc diagrams. We provide a bijection between the set…
Two-term tilting complexes for preprojective algebras of non-Dynkin type
Yuta Kimura, Yuya Mizuno
In this paper, we study two-term tilting complexes for preprojective algebras of non-Dynkin type. We show that there exist two families of two-term tilting complexes, which are res…
Simplicial complexes and tilting theory for Brauer tree algebras
Hideto Asashiba, Yuya Mizuno, Ken Nakashima
We study 2-term tilting complexes of Brauer tree algebras in terms of simplicial complexes. We show the symmetry and convexity of the simplicial complexes as lattice polytopes. Via…
Torsion pairs for quivers and the Weyl groups
Yuya Mizuno, Hugh Thomas
We give an interpretation of the map defined by Reading, which is a map from the elements of a Coxeter group to the -sortable elements, in terms of the representation theo…
Derived Picard groups of preprojective algebras of Dynkin type
Yuya Mizuno
In this paper, we study two-sided tilting complexes of preprojective algebras of Dynkin type. We construct the most fundamental class of two-sided tilting complexes, which has a gr…
Discreteness of silting objects and t-structures in triangulated categories
Takahide Adachi, Yuya Mizuno, Dong Yang
We introduce the notion of ST-pairs of triangulated subcategories, a prototypical example of which is the pair of the bound homotopy category and the bound derived category of a fi…
Classifying tilting complexes over preprojective algebras of Dynkin type
Takuma Aihara, Yuya Mizuno
We study tilting complexes over preprojective algebras of Dynkin type. We classify all tilting complexes by giving a bijection between tilting complexes and the braid group of the…
Higher APR tilting preserves -representation infiniteness
Yuya Mizuno, Kota Yamaura
We show that -APR tilting preserves -representation infiniteness for . Moreover, we show that these tilting modules provide different tilting modules for the c…
Classifying τ-tilting modules over preprojective algebras of Dynkin type
Yuya Mizuno
We study support -tilting modules over preprojective algebras of Dynkin type. We classify basic support -tilting modules by giving a bijection with elements in the correspond…
ν-stable τ-tilting modules
Yuya Mizuno
Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable support tau-tilting modules. For any finite dimensional selfinjective algebra Λ, we give bijections betwe…
On mutations of selfinjective quivers with potential
Yuya Mizuno
We study silting mutations (Okuyama-Rickard complexes) for selfinjective algebras given by quivers with potential (QPs). We show that silting mutation is compatible with QP mutatio…
A Gabriel-type theorem for cluster tilting
Yuya Mizuno
We study the relationship between -cluster tilting modules over representation finite algebras and the Euler forms. We show that the dimension vectors of cluster-indecomposa…
APR tilting modules and graded quivers with potential
Yuya Mizuno
We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potenti…