A higher dimensional Auslander-Iyama-Solberg correspondence

Autor:	Cruz, Tiago, Psaroudakis, Chrysostomos
Rok vydání:	2024
Předmět:	Mathematics - Representation Theory Mathematics - Rings and Algebras 16G10 16E10 16E65 (Primary) 16G50 20G43 16G20 16S50 18G25 (Secondary)
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:	http://arxiv.org/abs/2405.02736 Zobrazit plný text záznamu View this record from Arxiv