Journal of Differential Geometry

The structure of noncommutative deformations

Eli Hawkins

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Noncommutatively deformed geometries, such as the noncommutative torus, do not exist generically. I showed in a previous paper that the existence of such a deformation implies compatibility conditions between the classical metric and the Poisson bivector (which characterizes the noncommutativity). Here I present another necessary condition: the vanishing of a certain rank 5 tensor. In the case of a compact Riemannian manifold, I use these conditions to prove that the Poisson bivector can be constructed locally from commuting Killing vectors.

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J. Differential Geom., Volume 77, Number 3 (2007), 385-424.

First available in Project Euclid: 22 October 2007

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Hawkins, Eli. The structure of noncommutative deformations. J. Differential Geom. 77 (2007), no. 3, 385--424. doi:10.4310/jdg/1193074900.

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