Shuffle algebras for quivers as quantum groups

We define a quantum loop group $\mathbf{U}^+_Q$ associated to any quiver $Q = (I, E)$ and "generic" parameters, with generators indexed by $I \times \mathbb{Z}$ and explicit quadratic and cubic relations. We prove that $\mathbf{U}^+_Q$ is isomorphic to the (generic, small) shuffle algebra associated to the quiver $Q$ and hence, by [Neg21a], to the localized K-theoretic Hall algebra of $Q$. For the quiver with one vertex and g loops, this yields a presentation of the spherical Hall algebra of a (generic) smooth projective curve of genus g (invoking the results of [SV12]).