States in non-associative quantum mechanics: Uncertainty relations and   semiclassical evolution
  A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and semiclassical equations, based on general properties of quantum moments. 
Martin Bojowald, Suddhasattwa Brahma, Umut Buyukcam and Thomas Strobl
hep-th math-ph math.MP