theta-deformations as compact quantum metric spaces

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dc.creatorLi, Hanfeng
dc.date2003-11-27
dc.date2005-04-07
dc.date.accessioned2026-07-07T05:03:20Z
dc.date.available2026-07-07T05:03:20Z
dc.descriptionLet 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.
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0311500
dc.identifierhttp://arxiv.org/abs/math/0311500
dc.identifierComm. Math. Phys. 256 (2005), no. 1, 213--238
dc.identifierdoi:10.1007/s00220-005-1318-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69374
dc.subjectOperator Algebras
dc.subjectQuantum Algebra
dc.subject46L87,53C23,53C27,58B34
dc.titletheta-deformations as compact quantum metric spaces
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