  We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It
shares some features with the Immirzi parameter of four-dimensional loop
quantum gravity: it does not affect the equations of motion, but modifies the
Poisson brackets and the constraint algebra at the canonical level. We focus on
the length operator and show how to define it through non-commuting fluxes. We
compute its spectrum and show the effect of this Immirzi-like ambiguity.
Finally, we extend these considerations to 4d gravity and show how the
different topological modifications of the action affect the canonical
structure of loop quantum gravity.
