# rank (Lie algebra)

Let $\U0001d524$ be a finite dimensional Lie algebra^{}.
One can show that all Cartan subalgebras^{} $\U0001d525\subset \U0001d524$ have the same
dimension. The *rank* of $\U0001d524$ is defined to be this dimension.

Title | rank (Lie algebra) |
---|---|

Canonical name | RankLieAlgebra |

Date of creation | 2013-03-22 12:25:07 |

Last modified on | 2013-03-22 12:25:07 |

Owner | rmilson (146) |

Last modified by | rmilson (146) |

Numerical id | 12 |

Author | rmilson (146) |

Entry type | Definition |

Classification | msc 17B20 |

Defines | rank |