Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.09229 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911650267791360 |
|---|---|
| author | Schaumann, Gregor |
| author_facet | Schaumann, Gregor |
| contents | We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their categories of modules. This fusion product on the quiver modules induces a graded ring structure with duality and trace on the moduli spaces of semisimple quiver modules. Our approach allows to consider a class of relations on such fusion quivers that are compatible with the rigid monoidal structure. In particular we obtain a class of preprojective algebras with fusion product on their modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fusion Quivers Schaumann, Gregor Quantum Algebra Category Theory Representation Theory 18M20, 16G20, 18M05, 14J10 We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their categories of modules. This fusion product on the quiver modules induces a graded ring structure with duality and trace on the moduli spaces of semisimple quiver modules. Our approach allows to consider a class of relations on such fusion quivers that are compatible with the rigid monoidal structure. In particular we obtain a class of preprojective algebras with fusion product on their modules. |
| title | Fusion Quivers |
| topic | Quantum Algebra Category Theory Representation Theory 18M20, 16G20, 18M05, 14J10 |
| url | https://arxiv.org/abs/2307.09229 |