  Recently, E.Martinengo obtained results on obstructions to deformations of
Higgs pairs by describing an L-infinity morphism inducing the Hitchin map. In
this note we show that analogous results hold for principal G-Higgs bundles,
where G is a complex reductive group. We show that the L-infinity morphism has
a Lie-algebraic analogue inducing the adjoint quotient morphism.
