## Abstract

Let K be a (algebraically closed) field. A morphism A {long rightwards arrow from bar} g^{-1}Ag, where A ∈ M(n) and g ∈ GL(n), defines an action of a general linear group GL(n) on an n × n-matrix space M(n), referred to as an adjoint action. In correspondence with the adjoint action is the coaction α: K[M(n)] → K[M(n)] ⊗ K[GL(n)] of a Hopf algebra K[GL(n)] on a coordinate algebra K[M(n)] of an n × n-matrix space, dual to the conjugation morphism. Such is called an adjoint coaction. We give coinvariants of an adjoint coaction for the case where K is a field of arbitrary characteristic and one of the following conditions is satisfied: (1) q is not a root of unity; (2) char K = 0 and q = ±1; (3) q is a primitive root of unity of odd degree. Also it is shown that under the conditions specified, the category of rational GL_{q} × GL_{q}-modules is a highest weight category.

Original language | English |
---|---|

Pages (from-to) | 239-249 |

Number of pages | 11 |

Journal | Algebra and Logic |

Volume | 48 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 2009 |

Externally published | Yes |

## Keywords

- Adjoint action
- Adjoint coaction
- Field
- Rational module

## ASJC Scopus subject areas

- Analysis
- Logic