  The introduction of a non-abelian gauge group embedded into the rigid
symmetry group G of a field theory with abelian vector fields and no
corresponding charges, requires in general the presence of a hierarchy of
p-form gauge fields. The full gauge algebra of this hierarchy can be defined
independently of a specific theory and is encoded in the embedding tensor that
determines the gauge group. When applied to specific Lagrangians, the algebra
is deformed in an intricate way and in general will only close up to equations
of motion. The group-theoretical structure of the hierarchy exhibits many
interesting features, which have been studied starting from the low-p forms.
Here the question is addressed what happens generically for high values of p.
In addition a number of other features is discussed concerning the role that
the p-forms play in various deformations of the theory.
