Mathematics – Quantum Algebra
Scientific paper
2005-04-12
Mathematics
Quantum Algebra
36 pages, 1 figure. Expands upon my earlier paper math.QA/0211203
Scientific paper
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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