203 citations · 303 across the 19 of their papers we have counts for
19 papers
A note on a homological epimorphism whose source is a piecewise hereditary algebra
Takuma Aihara
We study a homological epimorphism of proper dg algebras and show that if the source is a finite dimensional piecewise hereditary algebra, then the target is derived equivalent to…
Examples of tilting-discrete symmetric algebras
Takuma Aihara
We give several examples of tilting-discrete symmetric algebras; in particular, one explores which algebra has tilting-discrete trivial extension. We provide a counter example of t…
Chiral Diffraction from Aperiodic Monotile Lattice
Yuto Moritake, Masato Takiguchi, Takuma Aihara +1
Aperiodic systems such as quasiperiodic systems exhibit unique properties different from periodic structures. In 2023, Smith et al. discovered a new aperiodic structure: a single-s…
When is the silting-discreteness inherited?
Takuma Aihara, Takahiro Honma
We explore when the silting-discreteness is inherited. As a result, one obtains that taking idempotent truncations and homological epimorphisms of algebras transmit the silting-dis…
A symmetry of silting quivers
Takuma Aihara, Qi Wang
We investigate symmetry of the silting quiver of a given algebra which is induced by an anti-automorphism of the algebra. In particular, one shows that if there is a primitive idem…
On representation-finite gendo-symmetric algebras with only one non-injective projective module
Takuma Aihara, Aaron Chan, Takahiro Honma
Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig a…
-tilting finite triangular matrix algebras
Takuma Aihara, Takahiro Honma
First, we give a new example of silting-discrete algebras. Second, one explores when the algebra of triangular matrices over a finite dimensional algebra is -tilting finite. In…
Report on the finiteness of silting objects
Takuma Aihara, Takahiro Honma, Kengo Miyamoto +1
We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, one studies two classes of -tilting-fi…
Remarks on dimensions of triangulated categories
Takuma Aihara, Ryo Takahashi
In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal…
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…
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…
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…
Endofunctors of singularity categories characterizing Gorenstein rings
Takuma Aihara, Ryo Takahashi
In this paper, we prove that certain contravariant endofunctors of singularity categories characterize Gorenstein rings.
Derived equivalences between symmetric special biserial algebras
Takuma Aihara
The notion of mutation plays crucial roles in representation theory of algebras. Two kinds of mutation are well-known: tilting/silting mutation and quiver-mutation. In this paper,…
Dimensions of triangulated categories with respect to subcategories
Takuma Aihara, Tokuji Araya, Osamu Iyama +2
This paper introduces the concept of the dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upp…
Generators and dimensions of derived categories
Takuma Aihara, Ryo Takahashi
Several years ago, Bondal, Rouquier and Van den Bergh introduced the notion of the dimension of a triangulated category, and Rouquier proved that the bounded derived category of co…
Tilting-connected symmetric algebras
Takuma Aihara
The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-…
Silting mutation in triangulated categories
Takuma Aihara, Osamu Iyama
In representation theory of algebras the notion of `mutation' often plays important roles, and two cases are well known, i.e. `cluster tilting mutation' and `exceptional mutation'.…
Mutating Brauer trees
Takuma Aihara
In this paper we introduce mutation of Brauer trees. We show that our mutation of Brauer trees explicitly describes the tilting mutation of Brauer tree algebras introduced by Okuya…