# algebraic torus

Let $k$ be a field. Then ${k}^{*}$, the multiplicative group^{} of $k$ is an affine algebraic group over $k$. An affine algebraic group of the form ${({k}^{*})}^{n}$ is called an algebraic torus over $k$.

The name is to the fact that if $k=\u2102$, then an algebraic torus is the complexification of the standard torus ${({S}^{1})}^{n}$.

Title | algebraic torus |
---|---|

Canonical name | AlgebraicTorus |

Date of creation | 2013-03-22 13:53:27 |

Last modified on | 2013-03-22 13:53:27 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 7 |

Author | bwebste (988) |

Entry type | Definition |

Classification | msc 14L17 |