EDAI

Let X and G be compact Lie groups, F1 : X ! X the time-one map of a C1 measure-preserving flow, : X ! G a continuous function and a finite-dimensional 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.

The absolute continuous spectrum of skew products of compact Lie groups
Rafael Tiedra de Aldecoa (PUC-Santiago, Chile)
Let X and G be compact Lie groups, F1 : X ! X the time-one map of a C1 measure-preserving flow, : X ! G a continuous function and a finite-dimensional 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.