On triangulated categories and enveloping algebras
On triangulated categories and enveloping algebras
复制标题
作者：
Fan Xu
利用\cite{XX2006}中对同构有限三角化范畴中产生的Hall代数的方法，我们发现了2周期三角化范畴中不可分解对象的“几乎”关联乘法结构。作为应用，我们给出了\cite{PX2000}中Peng和Xiao定理的一个新的证明，提供了一种通过2周期三角化范畴实现可对称的Kac-Moody代数和椭圆李代数的方法。
By using the approach in \cite{XX2006} to Hall algebras arising in homologically finite triangulated categories, we find an `almost' associative multiplication structure for indecomposable objects in a 2-periodic triangulated category. As an application, we give a new proof of the theorem of Peng and Xiao in \cite{PX2000} which provides a way of realizing symmetrizable Kac-Moody algebras and elliptic Lie algebras via 2-periodic triangulated categories.