Quantum loop groups for arbitrary quivers

Abstract

We study the dual constructions of quantum loop groups and Feigin-Odesskii type shuffle algebras for an arbitrary quiver, for which the arrow parameters are arbitrary non-zero elements of any field. Examples of our setup include $K$-theoretic Hall algebras of quivers with 0 potential, quantum loop groups of Kac-Moody type and quiver quantum toroidal algebras.