From representations of quivers via Hall and Loewy algebras to quantum groups
From representations of quivers via Hall and Loewy algebras to quantum groups
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DOI：
10.1090/conm/131.2/1175845
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发表时间：
1992
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影响因子：
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通讯作者：
C. Ringel
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文献类型：
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作者：
C. Ringel
设k是对称广义Cartan矩阵，g = g（k）是相应的具有三角分解的Kac-Moody李代数g = n− k h <$n+（见[K]）.记B+ = B+（n）= h <$n+为Borel子代数.设Uq（B+）是B+的泛包络代数的量子化，它由生成元和关系定义，我们将在下面回忆。对于有限型或仿射型的图，我们想利用箭图的表示理论，在[R2]，[R3]，[R4]和[R5]之后，研究Uq（B+）的构造。
Let ∆ be a symmetric generalized Cartan matrix, and g = g(∆) the corresponding Kac–Moody Lie–algebra with triangular decomposition g = n−⊕h⊕n+ (see [K]. We denote by b+ = b+(∆) = h ⊕ n+ the Borel subalgebra. Let Uq(b+) be the quantization of the universal enveloping algebra of b+, it is defined by generators and relations as we will recall below. For ∆ of finite or affine type, we want to survey a construction of Uq(b+) using the representation theory of quivers, following [R2], [R3], [R4] and [R5].