English

Claus Michael Ringel's main contributions to Gorenstein-projective modules

Representation Theory 2025-05-20 v1

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 \mho-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 An\mathbb A_n via submodule category; semi-Gorenstein-projective modules, reflexive modules, Koszul modules, as well as the Ω\Omega-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.

Keywords

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}
}
R2 v1 2026-07-01T02:20:35.673Z