# reductive

Let $G$ be a Lie group or algebraic group. $G$ is called reductive over a field $k$ if every representation of $G$ over $k$ is completely reducible

For example, a finite group^{} is reductive over a field $k$ if and only if its order is not divisible by the characteristic of $k$ (by Maschkeâ€™s theorem). A complex Lie group is reductive if and only if it is a direct product^{} of a semisimple group and an algebraic torus.

Title | reductive |
---|---|

Canonical name | Reductive |

Date of creation | 2013-03-22 13:23:49 |

Last modified on | 2013-03-22 13:23:49 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 6 |

Author | bwebste (988) |

Entry type | Definition |

Classification | msc 22C05 |