## Abstract

Let H be a Hopf algebra over a field k, and A an H-module algebra, with subalgebra of H-invariants denoted by A^{H}. When (H, R) is quasitriangular and A is quantum commutative with respect to (H, R), (e.g. quantum planes, graded commutative superalgebras), then [formula ommitted] center of A =Z(A). In this paper we are mainly concerned with actions of H for which A^{H}⊂ Z(A). We show that under this hypothesis there exists strong relations between the ideal structures of A^{H}, A and A#H. We demonstrate the theorems by constructing an example of a quantum commutative A, so that A/A^{H}is H*-Galois. This is done by giving (C G)*, G = Z_{n} X Z_{n},a nontrivial quasitriangular structure and defining an action of it on a localization of the quantum plane.

Original language | English |
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Pages (from-to) | 2859-2883 |

Number of pages | 25 |

Journal | Communications in Algebra |

Volume | 21 |

Issue number | 8 |

DOIs | |

State | Published - 1 Jan 1993 |

## ASJC Scopus subject areas

- Algebra and Number Theory