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The Structure of Noncommutative Deformations

Eli Hawkins
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Abstract

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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Eli Hawkins. 2006-07-13. The Structure of Noncommutative Deformations. https://arxiv.org/abs/math/0504232

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