A note on linearization of actions of finitely semisimple Hopf algebras on local algebras Original Research Article

Let H be a Hopf algebra over a field k and let H circle times operator A → A, h circle times operator a → h.a, be an action of H on a commutative local Noetherian kalgebra (A, m). We say that this action is linearizable if there exists a minimal system x1, …, xn of generators of the maximal ideal m such that h.xi ε kx1 + …+ kxn for all h ε H and i = 1, …, n. In the paper we prove that the actions from a certain class are linearizable (see Theorem 4), and we indicate some consequences of this fact.