  We derive the fully extended supersymmetry algebra carried by D-branes in a
massless type IIA superspace vacuum. We find that the extended algebra contains
not only topological charges that probe the presence of compact spacetime
dimensions but also pieces that measure non-trivial configurations of the gauge
field on the worldvolume of the brane. Furthermore there are terms that measure
the coupling of the non-triviality of the worldvolume regarded as a U(1)-bundle
of the gauge field to possible compact spacetime dimensions. In particular, the
extended algebra carried by the D-2-brane can contain the charge of a Dirac
monopole of the gauge field. In the course of this work we derive a set of
generalized Gamma-matrix identities that include the ones presently known for
the IIA case.
  In the first part of the paper we give an introduction to the basic notions
of Noether current algebras and charge algebras; furthermore we find a Theorem
that describes in a general context how the presence of a gauge field on the
worldvolume of an embedded object transforming under the symmetry group on the
target space alters the algebra of the Noether charges, which otherwise would
be the same as the algebra of the symmetry group. This is a phenomenon recently
found by Sorokin and Townsend in the case of the M-5-brane, but here we show
that it holds quite generally, and in particular also in the case of D-branes.
