Abelian Hall categories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911094790946816 |
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| author | Cautis, Sabin |
| author_facet | Cautis, Sabin |
| contents | To a quiver we associate a finite length monoidal abelian category which categorifies the corresponding preprojective K-theoretic Hall algebra of Varagnolo-Vasserot. The simples in this category provide a (dual) canonical basis of the Hall algebra. In particular, if the quiver is affine, this provides a basis for the positive half of the corresponding quantum toroidal algebra. We also show that this abelian category is naturally endowed with renormalized r-matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abelian Hall categories Cautis, Sabin Algebraic Geometry Mathematical Physics Representation Theory To a quiver we associate a finite length monoidal abelian category which categorifies the corresponding preprojective K-theoretic Hall algebra of Varagnolo-Vasserot. The simples in this category provide a (dual) canonical basis of the Hall algebra. In particular, if the quiver is affine, this provides a basis for the positive half of the corresponding quantum toroidal algebra. We also show that this abelian category is naturally endowed with renormalized r-matrices. |
| title | Abelian Hall categories |
| topic | Algebraic Geometry Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2508.04631 |