  For algebraic Anosov diffeomorphisms we first express the reduced leafwise
cohomology with respect to the unstable foliation in terms of finite
dimensional Lie algebra cohomology. We then prove a dynamical Lefschetz trace
formula for the induced action on this cohomology using a result of Nomizu. We
also consider generalized Anosov maps for which the cohomology in question is
no longer finite dimensional in general. Using the representation theory of
nilpotent Lie groups we still arrive at a meaningful definition of traces on
cohomology. Again we establish a dynamical Lefschetz trace formula.
