Structure theorems for rings  under certain coactions of a Hopf algebra

Gaetana RESTUCCIA; Rosanna UTANO

Article Details

Structure theorems for rings under certain coactions of a Hopf algebra

Authors:

Gaetana RESTUCCIA | Rosanna UTANO

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.427-436

Document Type:

Article

Publication Date:

2/2013

Document Language:

Turkish

Document ID (Org No.):

2000747603

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Keywords:

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]/(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 (Di(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 Di(yj) = dij(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.

 

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]/(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 (Di(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 Di(yj) = dij(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.

Article Details

Structure theorems for rings under certain coactions of a Hopf algebra

Authors:

Gaetana RESTUCCIA | Rosanna UTANO

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.427-436

Document Type:

Article

Publication Date:

2/2013

Document Language:

Turkish

Document ID (Org No.):

2000747603

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Hopf algebras

derivations

Jacobian criterion

Issues

Article Details

Structure theorems for rings under certain coactions of a Hopf algebra

Authors: Gaetana RESTUCCIA | Rosanna UTANO

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.427-436

Document Type: Article

Publication Date: 2/2013

Document Language: Turkish

Document ID (Org No.): 2000747603

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Hopf algebras

derivations

Jacobian criterion

Issues

Authors:

Gaetana RESTUCCIA | Rosanna UTANO

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2013 Vol.37 Issue 3, pp.427-436

Document Type:

Article

Publication Date:

2/2013

Document Language:

Turkish

Document ID (Org No.):

2000747603

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098