Turkish Journal of Mathematics
DOI
10.3906/mat-1107-30
Abstract
Let \{D_1,..., D_n\} be a system of derivations of a k-algebra A, k a field of characteristic p > 0, defined by a coaction \delta of the Hopf algebra H_c = k[X_1,..., X_n]/(X_1^p,..., X_n^p), c \in \{0,1\}, the Lie Hopf algebra of the additive group and the multiplicative group on A, respectively. If there exist x_1, \dots, x_n \in A, with the Jacobian matrix (D_i(x_j)) invertible, [D_i,D_j] = 0, D_i^p = cD_i, c \in \{0, 1\}, 1 \leq i, j \leq n, we obtain elements y_1,..., y_n \in A, such that D_i(y_j) = \delta_{ij}(1 + cy_i), using properties of H_c-Galois extensions. A concrete structure theorem for a commutative k-algebra A, as a free module on the subring A^{\delta} of A consisting of the coinvariant elements with respect to \delta, is proved in the additive case.
Keywords
Hopf algebras, derivations, Jacobian criterion
First Page
427
Last Page
436
Recommended Citation
RESTUCCIA, GAETANA and UTANO, ROSANNA
(2013)
"Structure theorems for rings under certain coactions of a Hopf algebra,"
Turkish Journal of Mathematics: Vol. 37:
No.
3, Article 6.
https://doi.org/10.3906/mat-1107-30
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss3/6
