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Poisson-Nijenhuis Groupoids
Reports on Mathematical Physics ( IF 0.8 ) Pub Date : 2019-12-01 , DOI: 10.1016/s0034-4877(19)30095-3
Apurba Das

We define multiplicative Poisson-Nijenhuis structures on a Lie groupoid which extends the notion of symplectic-Nijenhuis groupoid introduced by Stie23non and Xu. We also introduce a special class of Lie bialgebroid structure on a Lie algebroid $A$, called P-N Lie bialgebroid, which defines a hierarchy of compatible Lie bialgebroid structures on $A$. We show that under some topological assumption on the groupoid, there is a one-to-one correspondence between multiplicative Poisson-Nijenhuis structures on a Lie groupoid and P-N Lie bialgebroid structures on the corresponding Lie algebroid.

中文翻译:

Poisson-Nijenhuis Groupoids

我们在 Lie groupoid 上定义乘法 Poisson-Nijenhuis 结构,它扩展了 Stie23non 和 Xu 引入的辛-Nijenhuis groupoid 的概念。我们还在李代数$A$上引入了一类特殊的李双代数结构,称为PN Lie bialgebroid,它定义了$A$上兼容的李双代数结构的层次结构。我们表明,在群状体的一些拓扑假设下,李群状体上的乘法 Poisson-Nijenhuis 结构与相应的李代数体上的 PN Lie 双代数体结构之间存在一一对应的关系。
更新日期:2019-12-01
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