Reduced quiver quantum toroidal algebras

TL;DR

This paper describes the generators and relations of reduced quiver quantum toroidal algebras acting on BPS state spaces of toric Calabi-Yau threefolds, linking to K-theoretic Hall algebras.

Contribution

It provides a new presentation of reduced quiver quantum toroidal algebras and connects them to K-theoretic Hall algebras of toric Calabi-Yau threefolds.

Findings

Explicit generators-and-relations description of reduced quiver quantum toroidal algebras.

Connection established between these algebras and K-theoretic Hall algebras.

Description valid modulo torsion.

Abstract

We give a generators-and-relations description of the reduced versions of quiver quantum toroidal algebras, which act on the spaces of BPS states associated to (non-compact) toric Calabi-Yau threefolds X. As an application, we obtain a description of the K-theoretic Hall algebra of (the quiver with potential associated to) X, modulo torsion.