Θ-deformations as Quantum Compact Metric Spaces
نویسنده
چکیده
Let M be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n × n skew-symmetric matrices θ. The Mθ’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(Mθ), which defines a metric on the state space of C(Mθ). We show that when M is connected, this metric induces the weak-∗ topology. This means that Mθ is a quantum compact metric space in the sense of Rieffel.
منابع مشابه
Θ-deformations as Compact Quantum Metric Spaces
LetM be a compact spin manifold with a smooth action of the ntorus. Connes and Landi constructed θ-deformations Mθ of M , parameterized by n×n real skew-symmetric matrices θ. TheMθ’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(Mθ), which defines a metric on the state space of C(Mθ). We show th...
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