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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.12637 |
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| _version_ | 1866915291925053440 |
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| author | Gao, Nan Lu, Xue-Song Zhang, Pu |
| author_facet | Gao, Nan Lu, Xue-Song Zhang, Pu |
| contents | 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 $\mathbb A_n$ via submodule category; semi-Gorenstein-projective modules, reflexive modules, Koszul modules, as well as the $Ω$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Claus Michael Ringel's main contributions to Gorenstein-projective modules Gao, Nan Lu, Xue-Song Zhang, Pu Representation Theory 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 $\mathbb A_n$ via submodule category; semi-Gorenstein-projective modules, reflexive modules, Koszul modules, as well as the $Ω$-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. |
| title | Claus Michael Ringel's main contributions to Gorenstein-projective modules |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.12637 |