# Lie’s theorem

Let $\U0001d524$ be a finite dimensional complex solvable Lie algebra^{}, and $V$ a repesentation of $\U0001d524$. Then there exists an element of $V$ which is a simultaneous eigenvector^{} for all elements of $\U0001d524$.

Applying this result inductively, we find that there is a basis of $V$ with respect to which all elements of $\U0001d524$ are upper triangular.

Title | Lie’s theorem |
---|---|

Canonical name | LiesTheorem |

Date of creation | 2013-03-22 13:20:40 |

Last modified on | 2013-03-22 13:20:40 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 6 |

Author | bwebste (988) |

Entry type | Theorem |

Classification | msc 17B30 |