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The Derived Equivalence Classification of Representation-Finite Selfinjective Algebras

- H. Asashiba
- Mathematics
- 1 April 1999

On a Lift of an Individual Stable Equivalence to a Standard Derived Equivalence for Representation-Finite Self-injective Algebras

- H. Asashiba
- Mathematics
- 1 October 2003

We shall show that every stable equivalence (functor) between representation-finite self-injective algebras not of type (D3m,s/3,1) with m≥2, 3∤s lifts to a standard derived equivalence. This implies… Expand

A generalization of Gabriel's Galois covering functors and derived equivalences

- H. Asashiba
- Mathematics
- 29 July 2008

Let $G$ be a group acting on a category $\mathcal{C}$. We give a definition for a functor $F\colon \mathcal{C} \to \mathcal{C}'$ to be a $G$-covering and three constructions of the orbit category… Expand

On Interval Decomposability of 2D Persistence Modules

- H. Asashiba, M. Buchet, Emerson G. Escolar, K. Nakashima, M. Yoshiwaki
- Mathematics
- 13 December 2018

In persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. In multidimensional persistence it is known to be impossible to classify all indecomposable… Expand

Gluing derived equivalences together

- H. Asashiba
- Mathematics
- 1 April 2012

The Grothendieck construction of a diagram $X$ of categories can be seen as a process to construct a single category $\Gr(X)$ by gluing categories in the diagram together. Here we formulate diagrams… Expand

Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type

- H. Asashiba
- Mathematics
- 15 March 2002

On Approximation of $2$D Persistence Modules by Interval-decomposables

- H. Asashiba, Emerson G. Escolar, K. Nakashima, M. Yoshiwaki
- Mathematics
- 5 November 2019

In this work, we propose a new invariant for $2$D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the rank invariant. In… Expand

Matrix method for persistence modules on commutative ladders of finite type

- H. Asashiba, Emerson G. Escolar, Y. Hiraoka, H. Takeuchi
- MathematicsJapan Journal of Industrial and Applied…
- 30 June 2017

The theory of persistence modules on the commutative ladders $$CL_n(\tau )$$CLn(τ) provides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence… Expand

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