5 papers
Algebraic stability theorem for derived categories of zigzag persistence modules
Yasuaki Hiraoka, Yuichi Ike, Michio Yoshiwaki
We study distances on zigzag persistence modules from the viewpoint of derived categories and Auslander--Reiten quivers. The derived category of ordinary persistence modules is der…
Interleavings and Matchings as Representations
Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular,…
Field choice problem in persistent homology
Ippei Obayashi, Michio Yoshiwaki
This paper tackles the problem of coefficient field choice in persistent homology. When we compute a persistence diagram, we need to select a coefficient field before computation.…
On isomorphisms of generalized multifold extensions of algebras without nonzero oriented cycles
H. Asashiba, M. Kimura, K. Nakashima +1
Assume that a basic algebra over an algebraically closed field with a basic set of primitive idempotents has the property that for all . Le…
Decomposition theory of modules: the case of Kronecker algebra
Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki
Let be a finite-dimensional algebra over an algebraically closed field . For any finite-dimensional -module we give a general formula that computes the indecompos…