The Le Bruyn-Procesi theorem following Lusztig
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917079675830272 |
|---|---|
| author | Craw, Alastair Yamagishi, Ryo |
| author_facet | Craw, Alastair Yamagishi, Ryo |
| contents | For any quiver $Q$ and dimension vector $v$, Le Bruyn-Procesi proved that the invariant ring for the action of the change of basis group on the space of representations $\text{Rep}(Q,v)$ is generated by the traces of matrix products associated to cycles in the quiver. Lusztig generalised this to allow for vertices where the group acts trivially. Here we provide a simple new proof of Lusztig's theorem and determine the relations between his algebra generators for any quiver with relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08527 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Le Bruyn-Procesi theorem following Lusztig Craw, Alastair Yamagishi, Ryo Algebraic Geometry Representation Theory For any quiver $Q$ and dimension vector $v$, Le Bruyn-Procesi proved that the invariant ring for the action of the change of basis group on the space of representations $\text{Rep}(Q,v)$ is generated by the traces of matrix products associated to cycles in the quiver. Lusztig generalised this to allow for vertices where the group acts trivially. Here we provide a simple new proof of Lusztig's theorem and determine the relations between his algebra generators for any quiver with relations. |
| title | The Le Bruyn-Procesi theorem following Lusztig |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2312.08527 |