Let X and G be compact Lie groups, F1 : X ! X the timeone map of a C1 measurepreserving
flow, : X ! G a continuous function and a finitedimensional irreducible unitary representation
of G. Then, we prove that the skew products
T : X G ! X G; (x; g) 7!
??
F1(x); (x)
;
have purely absolutely continuous spectrum in the subspace associated to if has a Dinicontinuous
Lie derivative along the flow and if a matrix multiplication operator related to the
topological degree of has nonzero determinant. This result provides a simple, but general,
criterion for the presence of an absolutely continuous component in the spectrum of skew products
of compact Lie groups.
