Monopole star products are non-alternative
  Non-associative algebras appear in some quantum-mechanical systems, for instance if a charged particle in a distribution of magnetic monopoles is considered. Using methods of deformation quantization it is shown here, that algebras for such systems cannot be alternative, i.e. their associator cannot be completely anti-symmetric. 
Martin Bojowald, Suddhasattwa Brahma, Umut Buyukcam, Thomas Strobl
math-ph hep-th math.MP quant-ph