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pro vyhledávání: '"Asai, Sota"'
Autor:
Asai, Sota, Iyama, Osamu
For an abelian length category $\mathcal{A}$ with only finitely many isoclasses of simple objects, we have the wall-chamber structure and the TF equivalence in the dual real Grothendeick group $K_0(\mathcal{A})_\mathbb{R}^*=\operatorname{Hom}_\mathbb
Externí odkaz:
http://arxiv.org/abs/2404.13232
Autor:
Asai, Sota
In the representation theory of finite-dimensional algebras $A$ over a field, the classification of 2-term (pre)silting complexes is an important problem. One of the useful tool is the g-vector cones associated to the 2-term presilting complexes in t
Externí odkaz:
http://arxiv.org/abs/2201.09543
Autor:
Asai, Sota, Iyama, Osamu
We study two classes of torsion classes which generalize functorially finite torsion classes, that is, semistable torsion classes and morphism torsion classes. Semistable torsion classes are parametrized by the elements in the real Grothendieck group
Externí odkaz:
http://arxiv.org/abs/2112.14908
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Autor:
Asai, Sota
For a finite-dimensional algebra $A$ over a field $K$ with $n$ simple modules, the real Grothendieck group $K_0(\operatorname{\mathsf{proj}} A)_\mathbb{R}:=K_0(\operatorname{\mathsf{proj}} A) \otimes_\mathbb{Z} \mathbb{R} \cong \mathbb{R}^n$ gives st
Externí odkaz:
http://arxiv.org/abs/1905.02180
Autor:
Asai, Sota, Pfeifer, Calvin
In this paper, we study the relationship between wide subcategories and torsion classes of an abelian length category $\mathcal{A}$ from the point of view of lattice theory. Motivated by $\tau$-tilting reduction of Jasso, we mainly focus on intervals
Externí odkaz:
http://arxiv.org/abs/1905.01148
Autor:
Asai, Sota
A (semi)brick over an algebra $A$ is a module $S$ such that the endomorphism ring $\operatorname{\mathsf{End}}_A(S)$ is a (product of) division algebra. For each Dynkin diagram $\Delta$, there is a bijection from the Coxeter group $W$ of type $\Delta
Externí odkaz:
http://arxiv.org/abs/1712.08311
Autor:
Asai, Sota
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 study semibricks from the point of view of $\tau$-tilting theory. We cons
Externí odkaz:
http://arxiv.org/abs/1610.05860