复二维局部对称Kähler流形变量分离形变形量化的显式公式
微分几何
2024-03-12 v2 数学物理
math.MP
辛几何
摘要
我们通过变量分离形变形量化给出复二维非交换局部对称 Kähler 流形。通过求解 Hara-Sako 给出的递推关系系统，给出其星乘积的显式公式。在二维情形中，该递推关系系统给出对应于两个坐标的两类方程。由这两类递推关系可获得对称化与反对称化的递推关系。对称化者给出递推关系的解。由反对称化者得到解所满足的恒等式。利用本研究所得方法构造了 与 的星乘积，并验证了这些星乘积满足上述恒等式。
引用
@article{arxiv.2206.15266,
title = {Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric K\"{a}hler manifold},
author = {Taika Okuda and Akifumi Sako},
journal= {arXiv preprint arXiv:2206.15266},
year = {2024}
}
备注
34 pages, no figure; In v2, typos and errors are corrected. Two subsections are added in Section 2. The organization of Section 4 is corrected from two to three subsections. Section 5 and many references are added