31 citations · 75 across the 15 of their papers we have counts for
15 papers
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…
Quasi-hereditary rings are closed under taking block extensions
Takahide Adachi, Mayu Tsukamoto
In this paper, we give a sufficient condition for Morita context rings to be quasi-hereditary. As an application, we show that each block extension of a quasi-hereditary ring is al…
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…