A NOTE ON LINEARIZATION OF ACTIONS OF FINITELY SEMISIMPLE HOPF-ALGEBRAS ON LOCAL ALGEBRAS

Let H be a Hopf algebra over a field k and let H x A --> A, hx a --> h .a, be an action of H on a commutative local Noetherian k-algebra (A,m ). We say that this action is linearizable if there exists a minimal s ystem x(l),...,x(n) of generators of the maximal ideal m such that h.x (i)is an element of x(l) +...+ kx(n) for all h is an element of H and i = l,...,n. In the paper we prove that the actions from a certain cla ss are linearizable (see Theorem 4), and we indicate some consequences of this fact. (C) 1998 Elsevier Science B.V. All rights reserved.