不能被Drinfel'd Twists诱导的明星产品
Star Products that can not be induced by Drinfel'd Twists
摘要：
这是我硕士论文的最终版本。我证明，有没有扭曲星产品的2球和高属椒盐卷饼表面变形辛结构。其中一个关键的论点是，一个连通的紧辛流形赋予扭曲星的产品必须是一个齐性空间。此外，在这种情况下，存在一个李代数上的非退化r-矩阵，该李代数的李群在流形上传递有效地作用。我回顾了齐性空间的理论，特别是2-球面上传递有效作用的分类，并讨论了r-矩阵和Drinfel'd扭曲的概念。这篇论文的一些结果可以在arxiv.org上与Pierre Bieliavsky，Chiara Esposito和Stefan Waldmann一起以“Twist Star Products的障碍”为标题的预印本获得。
英文摘要：
This is the final version of my master thesis. I prove that there are no twist star products on the 2-sphere and on the higher genus pretzel surfaces deforming a symplectic structure. One of the key arguments is that a connected compact symplectic manifold endowed with a twist star product has to be a homogeneous space. Furthermore, there is a non-degenerate r-matrix on a Lie algebra whose Lie group is acting transitively and effectively on the manifold in this case. I recap the theory of homogeneous spaces, in particular the classification of transitive effective actions on the 2-sphere, and discuss the notion of r-matrices and Drinfel'd twists. Some results of this thesis are available as a preprint with Pierre Bieliavsky, Chiara Esposito and Stefan Waldmann on arxiv.org under the title "Obstructions for Twist Star Products".
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