In the case of canonical noncommutativity, evidence of some departures from Poincaré symmetry are
found both if
is a fixed tensor [213
, 516
] and if it is a fixed observer-independent matrix [161, 236, 100].
The possibility to preserve classical Poincaré symmetry is instead still not excluded in what was actually the
earliest approach [211
] based on
, where for
one seeks a formulation with richer algebraic
properties.