Generalised Gabriel-Roiter measure and thin representations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913610150707200 |
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| author | Krasula, Dominik |
| author_facet | Krasula, Dominik |
| contents | For Dynkin and Euclidean quivers, it is shown that Gabriel-Roiter measures of thin representations equal the induced chain length functions on the corresponding system of subquivers. This allows a combinatorial procedure to find a GR filtration of thin representations, showing that GR measures of thin representations are field-independent. It is proved that an indecomposable filtration of a thin representation is a GR filtration for a suitable choice of a length function on the category of finite-dimensional representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Gabriel-Roiter measure and thin representations Krasula, Dominik Representation Theory 16G20, 05E10 For Dynkin and Euclidean quivers, it is shown that Gabriel-Roiter measures of thin representations equal the induced chain length functions on the corresponding system of subquivers. This allows a combinatorial procedure to find a GR filtration of thin representations, showing that GR measures of thin representations are field-independent. It is proved that an indecomposable filtration of a thin representation is a GR filtration for a suitable choice of a length function on the category of finite-dimensional representations. |
| title | Generalised Gabriel-Roiter measure and thin representations |
| topic | Representation Theory 16G20, 05E10 |
| url | https://arxiv.org/abs/2402.05051 |