Poisson Lie Sigma模型

摘要：

Manin三元组（D; g; ~ g）是一个互不相交的双代数（g; ~ g），是这个双代数D = g ~ g的直和.如果相应的李群具有泊松结构，则称为泊松-李群。Poisson-Lie sigma模型是由Poisson向量场矩阵计算的作用量（式（3 - 13））。[3]我们推导出了使模型作用最小的极值场，从而给出了运动方程（3.19）。本文计算了几种6维Manin三元组的作用量和运动方程，并给出了每种4维Manin三元组的一般公式。6维Manin三元组是（sl（2; C）sl（2; C）; sl（2; C）; sl（2; C））、（sl（2; C）sl（2; C）; sl（2; C）、（sl（2; C）; su（2; C）; sb（2; C））和（sl（2; C）; sb（2; C）; su（2; C））。

英文摘要：

A Manin triples (D; g; ~ g) is a bialgebra (g; ~ g which don't intersect each others and a direct sum of this bialgebra D = g ~ g). If the corresponding Lie groups have a Poisson structure, they are called Poisson-Lie groups. A Poisson-Lie sigma models is an action (3.13) calculated by a Poisson vector eld matrix. [3] have deduced the extremal eld which minimize the action of this models, which gives the motion equation (3.19). We calculate here the action and the equations of motion for some 6-dimensionals Manin triples and we give a general formula for each 4-dimensional Manin triples. The 6-dimensional Manin triples are (sl(2; C) sl(2; C) ; sl(2; C); sl(2; C)),(sl(2; C) sl(2; C) ; sl(2; C)); sl(2; C),(sl(2; C); su(2; C); sb(2; C)) and (sl(2; C); sb(2; C); su(2; C)).

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