Claus Michael Ringel's main contributions to Gorenstein-projective modules
Abstract
In this article we try to recall Claus Michael Ringel's works on the Gorenstein-projective modules. This will involve but not limited to his fundamental contributions, such as in, the solution to the independence problem of totally reflexivity conditions; the technique of -quivers; a fast algorithm to obtain the Gorenstein-projective modules over the Nakayama algebras; the one to one correspondence between the indecomposable non-projective perfect differential modules of a quiver and the indecomposable representations of this quiver; the description of the module category of the preprojective algebras of type via submodule category; semi-Gorenstein-projective modules, reflexive modules, Koszul modules, as well as the -growth of modules, over short local algebras; and his negative answer to the question whether an algebra has to be self-injective in case all the simple modules are reflexive.
Cite
@article{arxiv.2505.12637,
title = {Claus Michael Ringel's main contributions to Gorenstein-projective modules},
author = {Nan Gao and Xue-Song Lu and Pu Zhang},
journal= {arXiv preprint arXiv:2505.12637},
year = {2025}
}