Journal of Differential Geometry

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.

Article information

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

Dates
First available in Project Euclid: 22 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1193074900

Digital Object Identifier
doi:10.4310/jdg/1193074900

Mathematical Reviews number (MathSciNet)
MR2362320

Zentralblatt MATH identifier
1130.53062

Citation

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


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