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arXiv · 2508.04631

Abelian Hall categories

Sabin Cautis
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Abstract

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.

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Sabin Cautis. 2025-08-06. Abelian Hall categories. https://arxiv.org/abs/2508.04631

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