6 citations · 13 across the 10 of their papers we have counts for
11 papers
Interleaving distances from height-difference functions on posets
Toshitaka Aoki
Interleaving distances provide a fundamental tool for comparing persistence modules and have been widely used in topological data analysis. Their definitions are typically based on…
Fans and polytopes in tilting theory III: Classification of convex -fans of rank 3
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
The -fan of a finite dimensional algebra is a non-singular fan in its real Grothendieck group, defined by tilting theory. If the union of the simplices a…
Dimensions of -tilting modules over path algebras and preprojective algebras of Dynkin type
Toshitaka Aoki, Yuya Mizuno
In this paper, we introduce a new generating function called -polynomial for the dimensions of -tilting modules over a given finite dimensional algebra. Firstly, we study bas…
Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
Recently, there is growing interest in the use of relative homology algebra to develop invariants using interval covers and interval resolutions (i.e., right minimal approximations…
Fans and polytopes in tilting theory II: -fans of rank 2
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
The -fan of a finite dimensional algebra is a fan in its real Grothendieck group defined by tilting theory. We give a classification of complete -fans of rank 2. More explici…
Fans and polytopes in tilting theory I: Foundations
Toshitaka Aoki, Akihiro Higashitani, Osamu Iyama +2
For a finite dimensional algebra over a field , the 2-term silting complexes of gives a simplicial complex called the -simplicial complex. We give tilting theo…
A complete classification of -tilting finite Schur algebras
Toshitaka Aoki, Qi Wang
In this paper, we determine the -tilting finiteness for some blocks of classical Schur algebras. Combining with the results in arXiv:2010.05206, we get a complete classification…
Brauer tree algebras have -tilting complexes
Toshitaka Aoki
We show that any Brauer tree algebra has precisely -tilting complexes, where is the number of edges of the associated Brauer tree. More explicitly, for an ex…
Complete gentle and special biserial algebras are -tame
Toshitaka Aoki, Toshiya Yurikusa
The -vectors of two-term presilting complexes are important invariants. We study a fan consisting of all -vector cones for a complete gentle algebra. We show that any complet…
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…
Classifying torsion classes for algebras with radical square zero via sign decomposition
Toshitaka Aoki
To study the set of torsion classes of a finite dimensional basic algebra, we use a decomposition, called sign-decomposition, parametrized by elements of where is…