Galois lattices (or concept lattices), which are lattices built on a binary relation, are now used in many fields, such as Data Mining and hierarchy organization, but may be of exponential size. In this paper, we propose a decomposition of a Galois sub-hierarchy which is of small size but contains useful inheritance information. We show how to efficiently maintain this information when an element is added to or removed from the relation, using a dynamic domination table which describes the underlying graph with which we encode the lattice.