Hochschild cohomology and characteristic classes for star products
Hochschild cohomology and characteristic classes for star products
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Hochschild 上同调和明星产品的特征类
DOI：
10.1090/trans2/186/07
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
P. Xu
中科院分区：
文献类型：
--
作者：
A. Weinstein;P. Xu
我们证明了辛流形上的形式变形量子化所得到的代数的Hochschild上同调同构于流形的de Rham上同调中系数的形式级数.通过区分相对于变形参数的星积得到的上同调类被认为是密切相关的特征类的量化。分析中的一个基本作用是由“量子刘维尔算子”发挥的，它以与刘维尔向量场缩放泊松结构（或作用单位）相同的方式重新缩放变形参数。给出了几个例子。
We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class obtained by differentiating the star-product with respect to the deformation parameter is seen to be closely related to the characteristic class of the quantization. A fundamental role in the analysis is played by ``quantum Liouville operators,'' which rescale the deformation parameter in the same way in which Liouville vector fields scale the Poisson structure (or the units of action). Several examples are given.