Year: 2022
Type: preprint
Abstract: Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective. This conjecture is an important part of the Nakayama conjecture. Our principal motivation of this work is a systematic understanding of finitely generated, orthogonal generators over a self-injective Artin algebra from the view point of stable module categories. As a result, for an orthogonal generator M, we establish a recollement of the M-relative stable categories, describe compact objects of the right term of the recollement, and give equivalent characterizations of Tachikawa's second conjecture in terms of M-Gorenstein categories. Further, we introduce Gorenstein-Morita algebras and show that the Nakayama conjecture holds true for them.
Source: arXiv (Cornell University)
Authors: Chen, Hongxing, Xi, Changchang
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2556339584, G4371076529
OpenAlex ID: W4294295609