Cluster χ-varieties, amalgamation, and Poisson—Lie groups
Cluster χ-varieties, amalgamation, and Poisson—Lie groups
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DOI：
10.1007/978-0-8176-4532-8_2
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发表时间：
2005-08
期刊：
影响因子：
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通讯作者：
V. Fock;A. Goncharov
中科院分区：
文献类型：
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作者：
V. Fock;A. Goncharov
本文从具有平凡中心的分裂半简单实李群g出发，定义了一类具有附加结构的簇。我们将它们描述为聚类χ-变异，如[FG2]所定义。特别是它们是泊松品种。我们将这些变体的正则泊松映射定义为具有V. Drinfeld在[D， D1]中定义的标准泊松-李结构的群。其中一个映射到群上，从而为g提供正则有理坐标。
In this paper, starting from a split semisimple real Lie groupGwith trivial center, we define a family of varieties with additional structures. We describe them ascluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varieties to the groupGequipped with the standard Poisson—Lie structure defined by V. Drinfeld in [D, D1]. One of them maps to the group birationally and thus providesGwith canonical rational coordinates.