论文标题
最简单的泊松Orbifold的变形量化
Deformation quantization of the simplest Poisson Orbifold
论文作者
论文摘要
每当给定的泊松歧管配备离散对称性时，对称函数的相应代数或对称组扭曲的函数代数都可以具有新的变形，而Kontsevich Formital并未捕获。我们考虑了这种情况的最简单示例：$ \ mathbb {r}^2 $带有反射对称$ \ mathbb {z} _2 $。通常的量化导致Weyl代数。尽管Weyl代数很僵硬，但由$ \ Mathbb {Z} _2 $ functions均匀或扭曲的代数具有另外一个变形，由Wigner识别，与Feigin的$GL_λ$和Fuzzy Sphere相关。在同源扰动理论的帮助下，我们获得了变形产品的明确公式，可以从shoikhet-tygan-kontsevich形式上提取其第一阶。
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by Kontsevich Formality. We consider the simplest example of this situation: $\mathbb{R}^2$ with the reflection symmetry $\mathbb{Z}_2$. The usual quantization leads to the Weyl algebra. While Weyl algebra is rigid, the algebra of even or twisted by $\mathbb{Z}_2$ functions has one more deformation, which was identified by Wigner and is related to Feigin's $gl_λ$ and to fuzzy sphere. With the help of homological perturbation theory we obtain explicit formula for the deformed product, the first order of which can be extracted from Shoikhet-Tsygan-Kontsevich formality.
