加权射影线的复合代数
Composition algebra of a weighted projective line
摘要：
本文研究了加权射影线上凝聚层范畴的Hall代数的合成子代数的约化Drinfeld二重的性质。本研究的动机是应用于某些李代数的量子化包络代数的理论。本文给出了单系型仿射李代数的量子化包络代数的一种新实现，并得到了这类代数之间的新嵌入。此外，我们的方法可以得到新的结果的结构上的环形代数的类型$D_4^{(1,1)}$，$E_6^{(1,1)}$，$E_7^{(1,1)}$和$E_8^{(1,1)}$的量化包络代数。特别是，我们的方法导致一个模块化的行动建设，并允许定义一类代数PBW型的基础。
英文摘要：
In this article, we deal with properties of the reduced Drinfeld double of the composition subalgebra of the Hall algebra of the category of coherent sheaves on a weighted projective line. This study is motivated by applications in the theory of quantized enveloping algebras of some Lie algebras. We obtain a new realization of quantized enveloping algebras of affine Lie algebras of simply-laced type and get new embeddings between such algebras. Moreover, our approach allows to derive new results on the structure of the quantized enveloping algebras of the toroidal algebras of types $D_4^{(1,1)}$, $E_6^{(1,1)}$, $E_7^{(1,1)}$ and $E_8^{(1,1)}$. In particular, our method leads to a construction of a modular action and allows to define a PBW-type basis for that classes of algebras.
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