4 papers
Interval endomorphism algebras of posets: Reedy structure, combinatorics, and homological theory
Toshitaka Aoki
Let be a finite connected poset and let be the opposite endomorphism algebra of the direct sum of all interval representations of over a field. Via projectivization,…
On preservation of relative resolutions for poset representations
Toshitaka Aoki, Shunsuke Tada
The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the ad…
Bipath Persistence
Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this se…
Mutation of Brauer configuration algebras
Toshitaka Aoki, Yingying Zhang
For Brauer graph algebras, tilting mutation is compatible with flip of Brauer graphs. The aim of this paper is to generalize this result to the class of Brauer configuration algebr…