Abelian Hall categories
Algebraic Geometry
2025-08-07 v1 Mathematical Physics
math.MP
Representation Theory
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.
Keywords
Cite
@article{arxiv.2508.04631,
title = {Abelian Hall categories},
author = {Sabin Cautis},
journal= {arXiv preprint arXiv:2508.04631},
year = {2025}
}