Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1107-30
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