Deformation quantization of Heisenberg manifolds
The author studies the deformation quantization for a smooth manifold equipped with a Poisson bracket in the \(C^*\)-algebra framework, as examples of non-commutative manifolds. The much studied non-commutative tori is shown to be an example of the strict form of deformation quantization in author's formulation. As main result of the paper, invariant Poisson structures of Heisenberg manifolds under the action of the Heisenberg Lie group are determined and found to fall into two types, leading to different structure of the resulting algebras for deformation quantization. Generalizations to more general situations are studied in detail. Finally, the SO(3) action of the 2-sphere is shown to be rigid, all deformation being commutative.
invariant Poisson structures of Heisenberg manifolds under the action of the Heisenberg Lie group
scientific article; zbMATH DE number 4113316
scientific article