31 citations · 75 across the 15 of their papers we have counts for
14 papers · 1 filter
Tilting theoretic approach to quasi-hereditary structures
Takahide Adachi, Aaron Chan, Yuta Kimura +1
A quasi-hereditary algebra is an algebra equipped with a certain partial order on its simple modules. Such a partial order -- called a quasi-hereditary structure -- gives…
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…
On -tilting theory
Takahide Adachi, Osamu Iyama, Idun Reiten
We give a brief introduction to -tilting theory [AIR]. In particular, we will see how our theory unifies two different branches of tilting theory, namely, silting theory and clu…
An assortment of properties of silting subcategories of extriangulated categories
Takahide Adachi, Mayu Tsukamoto
Extriangulated categories give a simultaneous generalization of triangulated categories and exact categories. In this paper, we study silting subcategories of an extriangulated cat…
Mixed standardization and Ringel duality
Takahide Adachi, Mayu Tsukamoto
Dlab--Ringel's standardization method gives a realization of a standardly stratified algebra. In this paper, we construct mixed stratified algebras, which are a generalization of s…
Hereditary cotorsion pairs and silting subcategories in extriangulated categories
Takahide Adachi, Mayu Tsukamoto
In this paper, we study (complete) cotorsion pairs in extriangulated categories. First, we study a relationship between an interval of the poset of cotorsion pairs and the poset of…
Intervals of -torsion pairs in extriangulated categories with negative first extensions
Takahide Adachi, Haruhisa Enomoto, Mayu Tsukamoto
As a general framework for the studies of -structures on triangulated categories and torsion pairs in abelian categories, we introduce the notions of extriangulated categories w…
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…
Tilting modules and dominant dimension with respect to injective modules
Takahide Adachi, Mayu Tsukamoto
In this paper, we study a relationship between tilting modules with finite projective dimension and dominant dimension with respect to injective modules as a generalization of resu…
The number of two-term tilting complexes over symmetric algebras with radical cube zero
Takahide Adachi, Toshitaka Aoki
In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a…
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…
Classification of two-term tilting complexes over Brauer graph algebras
Takahide Adachi, Takuma Aihara, Aaron Chan
Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an ap…
Characterizing τ-rigid-finite algebras with radical square zero
Takahide Adachi
In this paper, we give a characterization of tau-rigid-finite algebras with radical square zero in terms of the separated quivers, which is an analog of a famous characterization o…
The classification of τ-tilting modules over Nakayama algebras
Takahide Adachi
In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain int…