Quantum loop groups for symmetric Cartan matrices
Abstract
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.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Topics in Algebra
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Publisher
- Walter de Gruyter GmbH
- Publication date
- 5 February 2026
- Language
- EN