The Structure of Noncommutative Deformations

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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.
36 pages, 1 figure. Expands upon my earlier paper math.QA/0211203

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Quantum Algebra, Differential Geometry, Symplectic Geometry, 58B34; 46L65; 53D17

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http://salesiana.dossiersoluciones.com/handle/123456789/101198

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504232
 http://arxiv.org/abs/math/0504232

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arXiv