Universal central extensions of elliptic affine Lie algebras
Universal central extensions of elliptic affine Lie algebras
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DOI：
10.1063/1.530700
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发表时间：
1994-12
影响因子：
1.3
通讯作者：
M. Bremner
中科院分区：
文献类型：
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作者：
M. Bremner
设g是一个简单的复（有限维）李代数，R是紧致复代数曲线上的正则函数环，其中去掉了有限个点。考虑g <$CR形式的李代数;这些推广了Kac-Moody循环代数，因为对于亏格为零的曲线，有两个穿孔R <$C[t，t−1]。g R的泛中心扩张类似于无扭仿射Kac-Moody代数。根据卡塞尔定理，泛中心扩张的核与R模精确微分的Kahler微分线性同构。首先确定任何R的核的维数。限制与2，3，或4个特殊点删除的超椭圆曲线，核的基础是确定的。进一步限制到椭圆曲线与穿孔在两个点（订单的一个和两个在组法），我们明确确定的上循环给出的交换关系的普遍中央扩展。结果涉及Pollaczek多项式，这是…
Let g be a simple complex (finite dimensional) Lie algebra, and let R be the ring of regular functions on a compact complex algebraic curve with a finite number of points removed. Lie algebras of the form g⊗CR are considered; these generalize Kac–Moody loop algebras since for a curve of genus zero with two punctures R≂C[t,t−1]. The universal central extension of g⊗R is analogous to an untwisted affine Kac–Moody algebra. By Kassel’s theorem the kernel of the universal central extension is linearly isomorphic to the Kahler differentials of R modulo exact differentials. The dimension of the kernel for any R is determined first. Restricting to hyperelliptic curves with 2, 3, or 4 special points removed, a basis for the kernel is determined. Restricting further to an elliptic curve with punctures at two points (of orders one and two in the group law) we explicitly determine the cocycles which give the commutation relations for the universal central extension. The results involve Pollaczek polynomials, which ar...