
TL;DR
This paper constructs a finite length monoidal abelian category from a quiver that categorifies the preprojective K-theoretic Hall algebra, providing canonical bases and structures related to quantum toroidal algebras.
Contribution
It introduces a new abelian category associated with quivers that categorifies the Hall algebra and offers canonical bases for quantum groups.
Findings
Provides a categorification of the Hall algebra for quivers.
Establishes a basis for the positive half of quantum toroidal algebras.
Shows the abelian category has natural renormalized r-matrices.
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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