algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety approximation; Auslander-Buchweitz context; cotilting bimodule; determinantal ring; Donkin system; good comodule; good filtration; highest weight theory; Hopf algebra; Matijevic-Roberts type theorem; quasi-hereditary algebra; reductive algebraic group; Ringel's approximation; Schur algebra; tilting module; Weyl module 