A general framework is described which associates geometrical structures to any set of D finite-dimensional Hermitian matrices X ^a , a = 1, …, D. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and allows to extract the underlying classical space without requiring the limit of large matrices or representation theory. The approach is based on the previously introduced concept of quasi-coherent states. In particular, a concept of quantum Khler geometry arises naturally, which includes the well-known quantized coadjoint orbits such as the fuzzy sphere and fuzzy . A quantization map for quantum Khler geometries is established. Some examples of quantum geometries which are not Khler are identified, including the minimal fuzzy torus.

描述了将几何结构与D个有限维Hermitian矩阵X ^a，a = 1，…，D的任何集合相关联的通用框架。该框架将模糊空间的众所周知的示例进行了概括和系统化，并允许提取底层经典空间而无需大矩阵或表示理论的限制。该方法基于先前引入的准相干状态的概念。尤其是，自然出现了量子Khler几何概念，其中包括众所周知的量化共轭轨道，例如模糊球和模糊球。 。建立了量子Khler几何形状的量化图。确定了不是Khler的量子几何的一些示例，包括最小模糊环面。