A higher dimensional Auslander-Iyama-Solberg correspondence
Autor: | Cruz, Tiago, Psaroudakis, Chrysostomos |
---|---|
Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | In this paper, we prove a higher dimensional version of Auslander-Iyama-Solberg correspondence. Iyama and Solberg have shown a bijection between $n$-minimal Auslander-Gorenstein algebras and $n$-precluster tilting modules. If $A$ is an $n$-minimal Auslander-Gorenstein algebra, then the pair $(A,P)$ is a relative $(n+1)$-Auslander-Gorenstein pair in the sense of the authors, where $P$ is the minimal faithful projective-injective left $A$-module. We establish a higher dimensional Auslander-Iyama-Solberg, where $P$ is replaced by any self-orthogonal module $Q$ having finite projective and injective dimension. This new correspondence provides a bijection between relative Auslander--Gorenstein pairs and a new class of objects that generalise precluster tilting modules. This way, we obtain a new correspondence coming from the modular representation theory of general linear groups. Comment: 24 pages, comments are welcome! |
Databáze: | arXiv |
Externí odkaz: |