Infinitely many star products to play with

  title={Infinitely many star products to play with},
  author={Jos{\'e} M. Gracia-Bond́ıa and Fedele Lizzi and Giuseppe Marmo and Patrizia Vitale},
  journal={Journal of High Energy Physics},
While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x i ,x j ] = iθ ij . Here we present new classes of (non-formal) deformed products associated to linear Lie algebras of the kind [x i ,x j ] = ic ij k x k . For all possible three-dimensional cases, we define a new star product and discuss its properties. To complete the analysis of these novel noncommutative spaces, we introduce noncompact… 
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