Open Access
November 2007 The structure of noncommutative deformations
Eli Hawkins
J. Differential Geom. 77(3): 385-424 (November 2007). DOI: 10.4310/jdg/1193074900


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.


Download Citation

Eli Hawkins. "The structure of noncommutative deformations." J. Differential Geom. 77 (3) 385 - 424, November 2007.


Published: November 2007
First available in Project Euclid: 22 October 2007

zbMATH: 1130.53062
MathSciNet: MR2362320
Digital Object Identifier: 10.4310/jdg/1193074900

Rights: Copyright © 2007 Lehigh University

Vol.77 • No. 3 • November 2007
Back to Top