Noncommutative Rigidity

Details Noncommutative Rigidity Noncommutative Rigidity

2002-11-13

arxiv.org/abs/math/0211203v4

Mathematics

Quantum Algebra

27 pages. Serious typo corrected from v3

Scientific paper

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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