M. Boratynski et A. Tyc, A NOTE ON LINEARIZATION OF ACTIONS OF FINITELY SEMISIMPLE HOPF-ALGEBRAS ON LOCAL ALGEBRAS, Journal of pure and applied algebra, 130(3), 1998, pp. 217-222
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.