Nilpotence and the generalized uncertainty principle(s)

We point out that some of the proposed generalized/modified uncertainty principles originate from solvable, or nilpotent at appropriate limits, “deformations” of Lie algebras. We briefly comment on formal aspects related to the well-posedness of one of these algebras. We point out a potential relation of such algebras with Classical Mechanics in the spirit of the symplectic non-squeezing theorem. We also point out their relation to a hierarchy of generalized measure theories emerging in a covariant formalism of quantum gravity.