algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety deformation theory; representations of finitely generated groups; algebraic group; variety; real points; lattice; semisimple Lie group; fundamental group; compact Kähler manifold; monodromy representation; polarized Hodge structure; Margulis superrigidity theorem; hyperbolic manifolds; totally geodesic hypersurfaces; flat connections 