  The notions of complementability and maximality were introduced in 1974 by
Ornstein and Weiss in the context of the automorphisms of a probability space,
in 2008 by Brossard and Leuridan in the context of the Brownian filtrations,
and in 2017 by Leuridan in the context of the poly-adic filtrations indexed by
the non-positive integers. We present here some striking analogies and also
some differences existing between these three contexts.
