Semisimple Lie algebras are far from flexibly C-stable, semisimple Lie groups and higher-rank lattices are not strictly C-stable, and free groups are not uniformly flexibly F-stable over any field.
Rank-st ability of polynomial equations
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Uniform rank metric stability of Lie algebras and groups
Semisimple Lie algebras are far from flexibly C-stable, semisimple Lie groups and higher-rank lattices are not strictly C-stable, and free groups are not uniformly flexibly F-stable over any field.