Star products, duality and double Lie algebras
  Quantization of classical systems using the star-product of symbols of observables is discussed. In the star-product scheme an analysis of dual structures is performed and a physical interpretation is proposed. At the Lie algebra level duality is shown to be connected to double Lie algebras. The analysis is specified to quantum tomography. The classical tomographic Poisson bracket is found. 
Olga V. Man'ko, Vladimir I. Man'ko, Giuseppe Marmo, Patrizia Vitale