论文标题
KLR代数的折叠
Foldings of KLR algebras
论文作者
论文摘要
令$ {\ mathbf u}^-_ q $为与kac-moody代数$ {\ mathfrak g} $相关的量子组的负一半，而$ \ useverline {\ mathbf u}^-_ q $由$ {\ mathfrak g} $折叠获得的量子组。令$ {\ mathbf a} = {\ mathbf z} [q，q^{ - 1}] $。麦克纳马拉（McNamara）表明，$ \下划线{\ mathbf u}^-_ q $通过$ {\ mathbf a} $的特定伸日戒指$ \ widetilde {\ mathbf a} $进行分类，并通过klr algebras的折叠理论。他提出了一个问题。在本文中，我们为这个问题给出了肯定的答案。
Let ${\mathbf U}^-_q$ be the negative half of the quantum group associated to a Kac-Moody algebra ${\mathfrak g}$, and $\underline{\mathbf U}^-_q$ the quantum group obtained by a folding of ${\mathfrak g}$. Let ${\mathbf A} = {\mathbf Z}[q,q^{-1}]$. McNamara showed that $\underline{\mathbf U}^-_q$ is categorified over a certain extenion ring $\widetilde{\mathbf A}$ of ${\mathbf A}$, by uing the folding theory of KLR algebras. He posed a question whether $\widetilde{\mathbf A}$ coincides with ${\mathbf A}$ or not. In this paper, we give an affirmative answer for this problem.
