李群上与左不变度量相关的谱三元组的乘法变形
Multiplicative deformations of spectrale triples associated to left invariant metrics on Lie groups
摘要：
本文研究三重$(G,π,\prs)$，其中$G$是一个连通和单连通的李群，$π$和$\prs$分别是$G$上的乘性Poisson张量和左不变黎曼度量，使得Hawkins提出的与$\prs$相关联的谱三重存在非交换变形（在$π$方向上）的必要条件得到满足.我们表明，这样的三元组$(G,π,\prs)$的分类的几何问题是等价的代数之一。我们解决这个代数问题，在低维，我们给列表中的所有$(G,π,\prs)$满足霍金斯的条件，到4维。
英文摘要：
We study the triple $(G,π,\prs)$ where $G$ is a connected and simply connected Lie group, $π$ and $\prs$ are, respectively, a multiplicative Poisson tensor and a left invariant Riemannian metric on $G$ such that the necessary conditions, introduced by Hawkins, to the existence of a non commutative deformation (in the direction of $π$) of the spectrale triple associated to $\prs$ are satisfied. We show that the geometric problem of the classification of such triple $(G,π,\prs)$ is equivalent to an algebraic one. We solve this algebraic problem in low dimensions and we give the list of all $(G,π,\prs)$ satisfying Hawkins's conditions, up to dimension four.
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