Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.05051 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913610150707200 |
|---|---|
| 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 |