A comparison between Rieffel’s and Kontsevich’s deformation quantizations for linear Poisson tensors
A comparison between Rieffel’s and Kontsevich’s deformation quantizations for linear Poisson tensors
复制标题
线性泊松张量的 Rieffel 和 Kontsevich 变形量化之间的比较
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
N. B. Amar
中科院分区：
文献类型：
--
作者：
N. B. Amar
我们考虑里费尔？的形变量子化和Kontsevich？s的星星积。我们给出了这些星星乘积之间的等价算符，并比较了这两个主要形变量子化例子的性质。我们展示了里费尔？s变形可以通过考虑定向图G得到。我们还证明孔采维奇？s的星星积通过一般李代数g上的C8紧支集函数在空间Cc 8（g）上的部分嵌入提供了一个变形量子化，以及幂零李代数g的对偶g* 上的Schwartz函数在空间S（g*）上的严格变形量子化.最后，我们给出了这两个星星积的显式公式，并推导了出现在这些表达式中的图的权。
We consider Rieffel?s deformation quantization and Kontsevich?s star product on the duals of Lie algebras equipped with linear Poisson brackets. We give the equivalence operator between these star products and compare properties of these two main examples of deformation quantization. We show that Rieffel?s deformation can be obtained by considering oriented graphs G. We also prove that Kontsevich?s star product provides a deformation quantization by partial embeddings on the space Cc8(g) of C8 compactly supported functions on a general Lie algebra g and a strict deformation quantization on the space S(g*) of Schwartz functions on the dual g* of a nilpotent Lie algebra g. Finally, we give the explicit formulae of these two star products and we deduce the weights of graphs occurring in these expressions.