非对易空间中的笛卡尔与克莱因相遇
Meeting Descartes and Klein Somewhere in a Noncommutative Space
摘要：
通过对非交换坐标代数对称性的研究，将坐标方法和Erlangen程序结合在非交换几何的框架下。作为模型，我们使用相干态结构和小波变换的功能空间。新的例子是一个三维频谱的非正规矩阵和一个量化程序从symplectomorphisms。保留字：海森堡群，特殊线性群，辛群，哈代空间，Segal-Bargmann空间，Clifford代数，柯西-黎曼-狄拉克算子，莫比乌斯变换，泛函演算，Weyl演算（量子化），量子力学，薛定谔表示，元表示。
英文摘要：
We combine the coordinate method and Erlangen program in the framework of noncommutative geometry through an investigation of symmetries of noncommutative coordinate algebras. As the model we use the coherent states construction and the wavelet transform in functional spaces. New examples are a three dimensional spectrum of a non-normal matrix and a quantisation procedure from symplectomorphisms. Keywords: Heisenberg group, special linear group, symplectic group, Hardy space, Segal-Bargmann space, Clifford algebra, Cauchy-Riemann-Dirac operator, Möbius transformations, functional calculus, Weyl calculus (quantization), quantum mechanics, Schrödinger representation, metaplectic representation.
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