Compatible Lie brackets related to elliptic curve
Compatible Lie brackets related to elliptic curve
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DOI：
10.1063/1.2158434
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发表时间：
2005-06
影响因子：
1.3
通讯作者：
A. Odesskii;Vladimir Sokolov
中科院分区：
文献类型：
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作者：
A. Odesskii;Vladimir Sokolov
对于sln的多个副本的直和，构造了一族与初始李括号相容的李括号。这些括号的结构常数用与椭圆曲线相关的θ函数表示。研究了这些括号的Casimir元的结构。本文将这种构造推广到向量值θ-函数的情形。讨论了基于二次Poisson括号的变元移位方法构造相容李括号的一种不同方法。
For the direct sum of several copies of sln, a family of Lie brackets compatible with the initial one is constructed. The structure constants of these brackets are expressed in terms of θ functions associated with an elliptic curve. The structure of Casimir elements for these brackets is investigated. A generalization of this construction to the case of vector-valued θ-functions is presented. A different procedure for constructing compatible Lie brackets based on the argument shift method for quadratic Poisson brackets is discussed.