# Lie element

Given a Lie algebra^{} $\U0001d524$ and its univeral enveloping algebra
$\U0001d518(\U0001d524)$, then an element $x\in \U0001d518(\U0001d524)$ is called
a *Lie element* if $x$ is in the image of $\U0001d524$ in $\U0001d518(\U0001d524)$.

This term is most often used for free Lie algebras and specifically in the famous Baker-Campbell-Hausdorff formula (theorem).

Title | Lie element |
---|---|

Canonical name | LieElement |

Date of creation | 2013-03-22 16:51:14 |

Last modified on | 2013-03-22 16:51:14 |

Owner | Algeboy (12884) |

Last modified by | Algeboy (12884) |

Numerical id | 4 |

Author | Algeboy (12884) |

Entry type | Definition |

Classification | msc 17B35 |

Classification | msc 16S30 |

Defines | Lie element |