论文标题
对称cartan矩阵的量子循环基团
Quantum loop groups for symmetric Cartan matrices
论文作者
论文摘要
我们介绍了与一般对称的Cartan矩阵相关的量子循环组，通过在通常的发电机之间施加足够的关系$ \ {e_ {e_ {i，k}，f_ {i，k} _ {i \ in i，k \ in i，k \ in \ mathb {z}} $ natural Hopf和pottral potter to pottral and potter and potter and potter and potter and pottral of pottral um the um。作为一个应用程序，我们描述了任何没有循环的颤抖者的本地化k理论厅代数，并具有特别重要的$ \ mathbb {c}^*$ Action。
We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators $\{e_{i,k}, f_{i,k}\}_{i \in I, k \in \mathbb{Z}}$ 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 $\mathbb{C}^*$ action.
