8 citations · 21 across the 13 of their papers we have counts for
14 papers
Mutations of simple-minded collections revisited
Sota Asai
Simple-minded collections in the bounded derived category are necessary tools in tilting theory of finite dimensional algebra…
Left modularity and extremality for (some) infinite lattices
Sota Asai, Osamu Iyama, Kaveh Mousavand +1
For some important families of complete infinite lattices, we study some generalizations of two fundamental notions which are mostly treated for finite lattices. Specifically, for…
The interval neighborhoods in the real Grothendieck groups
Sota Asai
For a finite dimensional algebra , the TF equivalence on the real Grothendieck group can be regarded as a completion of the -…
Bicompact torsion classes and conjectures on brick infinite algebras
Sota Asai
In the category of finitely generated modules over a finite dimensional algebra , a torsion class $\mathcal{T} \subset \operatorname{\mathsf{mod}…
Brick-splitting Torsion Pairs and Left Modularity
Sota Asai, Osamu Iyama, Kaveh Mousavand +1
We introduce the notion of brick-splitting torsion pairs as a modern analogue and generalization of the classical notion of splitting torsion pairs. A torsion pair is called brick-…
Maximal finite semibricks consist only of open bricks
Sota Asai
A semibrick is a set of modules satisfying Schur's Lemma, and it is said to be maximal if it is not properly contained in another semibrick. For any finite dimensional algebra $\va…
-TF equivalences on the real Grothendieck groups
Sota Asai, Osamu Iyama
For an abelian length category with only finitely many isoclasses of simple objects, we have the wall-chamber structure and the TF equivalence on the dual real Grothe…
Non-rigid regions of real Grothendieck groups of gentle and special biserial algebras
Sota Asai
In the representation theory of finite-dimensional algebras over a field, the classification of 2-term (pre)silting complexes is an important problem. One of the useful tool is…
Semistable torsion classes and canonical decompositions in Grothendieck groups
Sota Asai, Osamu Iyama
We study two classes of torsion classes which generalize functorially finite torsion classes, that is, semistable torsion classes and morphism torsion classes. Semistable torsion c…
The wall-chamber structures of the real Grothendieck groups
Sota Asai
For a finite-dimensional algebra over a field with simple modules, the real Grothendieck group $K_0(\operatorname{\mathsf{proj}} A)_\mathbb{R}:=K_0(\operatorname{\maths…
Wide subcategories and lattices of torsion classes
Sota Asai, Calvin Pfeifer
In this paper, we study the relationship between wide subcategories and torsion classes of an abelian length category from the point of view of lattice theory. Motiva…
Bricks over preprojective algebras and join-irreducible elements in Coxeter groups
Sota Asai
A (semi)brick over an algebra is a module such that the endomorphism ring is a (product of) division algebra. For each Dynkin diagram …
Semibricks
Sota Asai
In representation theory of finite-dimensional algebras, (semi)bricks are a generalization of (semi)simple modules, and they have long been studied. The aim of this paper is to stu…
The Grothendieck groups and stable equivalences of mesh algebras
Sota Asai
We deal with the finite-dimensional mesh algebras given by stable translation quivers. These algebras are self-injective, and thus the stable categories have a structure of triangu…