  The gauge transformations of p-form fields in supergravity theories acquire a
non-commuting character when one introduces potentials both for the theory's
original field strengths and for their duals. This has previously been shown in
the ``doubled'' formalism for maximal supergravities, where a generalised
duality relation between original and dual field strengths replaces the
equations of motion. In the doubled formalism, the gauge transformations
generate a superalgebra, and the corresponding symmetries have accordingly been
called ``superdualities.'' The corresponding Noether charges form a
representation of the cohomology ring on the spacetime manifold. In this paper,
we show that the gauge symmetry superalgebra implies certain non-trivial
relations among the various p-brane tensions, which can straightforwardly be
read off from the superalgebra commutation relations. This provides an elegant
derivation of the brane-tension relations purely within a given theory, without
the need to make use of duality relations between different theories, such as
the type IIA/IIB T-duality, although the results are consistent with such
dualities. We present the complete set of brane-tension relations in M-theory,
in the type IIA and type IIB theories, and in all the lower-dimensional maximal
supergravities. We also construct a doubled formalism for massive type IIA
supergravity, and this enables us to obtain the brane-tension relations
involving the D8-brane, purely within the framework of the massive IIA theory.
We also obtain explicit transformations for the nine-dimensional T-duality
between the massive type IIA theory and the Scherk-Schwarz reduced type IIB
theory.
