Structure theorems for rings under certain coactions of a Hopf algebra

Authors : Gaetana RESTUCCIA, Rosanna UTANO

Pages : 427-436

Doi:10.3906/mat-1107-30

View : 12 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let \{D1,..., Dn\} be a system of derivations of a k-algebra A, k a field of characteristic p > 0, defined by a coaction d of the Hopf algebra Hc = k[X1,..., Xn]/insert ignore into journalissuearticles values(X1p,..., Xnp);, c \in \{0,1\}, the Lie Hopf algebra of the additive group and the multiplicative group on A, respectively. If there exist x1, \dots, xn \in A, with the Jacobian matrix insert ignore into journalissuearticles values(Diinsert ignore into journalissuearticles values(xj);); invertible, [Di,Dj] = 0, Dip = cDi, c \in \{0, 1\}, 1 \leq i, j \leq n, we obtain elements y1,..., yn \in A, such that Diinsert ignore into journalissuearticles values(yj); = dijinsert ignore into journalissuearticles values(1 + cyi);, using properties of Hc-Galois extensions. A concrete structure theorem for a commutative k-algebra A, as a free module on the subring Ad of A consisting of the coinvariant elements with respect to d, is proved in the additive case.
Keywords : Hopf algebras, derivations, Jacobian criterion