Noncommutative projective curves and quantum loop algebras
Noncommutative projective curves and quantum loop algebras
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DOI：
10.1215/s0012-7094-04-12114-1
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发表时间：
2002-05
影响因子：
2.5
通讯作者：
O. Schiffmann
中科院分区：
文献类型：
--
作者：
O. Schiffmann
我们推广了Kapranov的一个定理，证明了有限域上加权射影线上相干束范畴的Hall代数提供了相应的Kac-Moody代数的仿射化的某个幂零子代数的（量子化）包络代数的实现。特别地，这产生了D_4， E_6， E_7或E_8类型的2-环面（或椭圆）代数的量化包络代数的一个几何实现，它是用属1的加权投影线表示的。
We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent subalgebra of the affinization of the correponding Kac-Moody algebra. In particular this yieds a geometric realization of the quantized enveloping algebra of 2-toroidal (or elliptic) algebras of types D_4, E_6, E_7 or E_8 in terms of weighted projective lines of genus one.