  We revisit Margulis-Zimmer Super-Rigidity and provide some generalizations.
In particular we obtain super-rigidity results for lattices in higher-rank
groups or product of groups, targeting at algebraic groups over arbitrary
fields with absolute values. We also obtain cocycle super-rigidity results for
a wide class of groups with respect to mixing actions. Our approach is based on
a systematic study of algebraic representations of ergodic actions.
