  The symmetry algebra of a QFT in the presence of an external EM background
(named "residual symmetry") is investigated within a Lie-algebraic, model
independent scheme. Some results previously encountered in the literature are
here extended. In particular we compute the symmetry algebra for a constant EM
background in D=3 and D=4 dimensions. In D= 3 dimensions the residual symmetry
algebra is isomorphic to $u(1)\oplus {\cal P}_c(2)$, with ${\cal P}_c(2)$ the
centrally extended 2-dimensional Poincar\'e algebra. In D=4 dimension the
generic residual symmetry algebra is given by a seven-dimensional solvable Lie
algebra which is explicitly computed. Residual symmetry algebras are also
computed for specific non-constant EM backgrounds.
