theta-deformations as compact quantum metric spaces

Details theta-deformations as compact quantum metric spaces theta-deformations as compact quantum metric spaces

2003-11-27

arxiv.org/abs/math/0311500v3

Comm. Math. Phys. 256 (2005), no. 1, 213--238

Mathematics

Operator Algebras

26 pages

Scientific paper

10.1007/s00220-005-1318-5

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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