Exterior products of compact quantum metric spaces.

Abstract: The theory of compact quantum metric spaces was initiated by Rieffel in the late nineties. Important inspiration came from the fundamental observation of Connes saying that the metric on a compact spin manifold can be recovered from the Dirac operator. A compact quantum metric space is an operator system (e.g. a unital C*-algebra) equipped with a seminorm which metrizes the weak-*-topology on the state space via the associated Monge-Kantorovich metric. In this talk we study tensor products of compact quantum metric spaces with specific focus on seminorms arising from the exterior product of spectral triples. On our way we obtain a novel characterization of compact quantum metric spaces using finite dimensional approximations and we apply this characterization to propose a completely bounded version of the theory.

mathematical physicscategory theorydifferential geometryfunctional analysisK-theory and homologyoperator algebrasquantum algebra

Audience: researchers in the discipline

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