We show that several standard associative quantizations in mathematical physics can be
expressed as cochain module-algebra twists in the spirit of Moyal products at least to O 3,
but to achieve this we twist not by a 2-cocycle but by a 2-cochain. This implies a hidden
nonassociativity not visible in the algebra itself but present in its deeper noncommutative
differential geometry, a phenomenon first seen in our previous work on semiclassicalization
of differential structures. The quantizations are induced by a classical group covariance and …