Year: 2026
Type: article
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 \{e_{i,k},f_{i,k}\}_{i\in I,\,k\in\mathbb{Z}} 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 ∗ \mathbb{C}^{*} action.
Author: Andrei Neguț
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7129097052