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Noncommutative Rigidity

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Abstract

Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions can be expressed as a system of partial differential equations relating the metric and the Poisson structure that describes the noncommutativity. I illustrate this by computing the obstructions for well known examples of noncommutative geometries and quantum groups. These rigid conditions may cast doubt on the idea of noncommutatively deformed space-time.

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  1. Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 4, 34014, Trieste, Italy

    Eli Hawkins

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  1. Eli Hawkins
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Hawkins, E. Noncommutative Rigidity. Commun. Math. Phys. 246, 211–235 (2004). https://doi.org/10.1007/s00220-004-1036-4

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