二维欧几里得和(1 + 1)poincarÉ基团上泊松-李结构的线性化

Q3 Mathematics Ural Mathematical Journal Pub Date : 2021-12-30 DOI:10.15826/umj.2021.2.002

Bousselham Ganbouri, Mohamed Wadia Mansouri

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摘要

本文讨论了（1+1）Poincaré和（2D\）Euclidean群上Poisson-Lie结构的线性化问题。我们构造了所有这些泊松李结构的坐标线性化的显式形式。为此，我们通过首先确定的它们的李代数上的李双代数结构的对应关系，计算了上面提到的这两个群上的所有泊松李结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS

The paper deals with linearization problem of Poisson-Lie structures on the \((1+1)\) Poincaré and \(2D\) Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebra structures on their Lie algebras which we first determine.

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