7 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
A torsion class of the module category of a finite dimensional algebra over a field is said to be compact if there exists a mo…
-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…
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…