  We classify compact K\"ahler manifolds $M$ of dimension $n\geq 3$ on which
acts a lattice of an almost simple real Lie group of rank $\geq n-1$. This
provides a new line in the so-called Zimmer program, and characterizes certain
type of complex tori by a property of their automorphisms groups.

Algebraic Geometry;Differential Geometry;Dynamical Systems