紧量子度量空间的θ-形变
theta-deformations as compact quantum metric spaces
摘要：
设M是紧自旋流形，其n-torus作用是光滑的. Connes和Landi构造了M的θ-变形M_{theta}，参数为n乘n实反对称矩阵θ。M上的M_{theta}和正则Dirac算子（D，H）是M的等谱变形.狄拉克算子D在C（M_{theta}）上定义了一个Lipschitz算子，它在C（M_{theta}）的状态空间上定义了一个度量。我们证明了当M是连通的时，这个度量导致弱-* 拓扑。这意味着M_{theta}是Rieffel意义下的紧致量子度量空间。
英文摘要：
Let M be a compact spin manifold with a smooth action of the n-torus. Connes and Landi constructed theta-deformations M_{theta} of M, parameterized by n by n real skew-symmetric matrices theta. The M_{theta}'s together with the canonical Dirac operator (D, H) on M are an isospectral deformation of M. The Dirac operator D defines a Lipschitz seminorm on C(M_{theta}), which defines a metric on the state space of C(M_{theta}). We show that when M is connected, this metric induces the weak-* topology. This means that M_{theta} is a compact quantum metric space in the sense of Rieffel.
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