Abstract We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators e i, k, f i, k i ∈ I, k ∈ Z \e₈, ₊, f₈, ₊\₈ ₈, \, ₊ in order for the natural Hopf pairing between the positive and negative halves of the quantum loop group to be perfect. As an application, we describe the localized 𝐾-theoretic Hall algebra of any quiver without loops, endowed with a particularly important C ∗ C^* action.
Andrei Neguţ (Thu,) studied this question.