### Abstract

We prove a version of the Poincaré-Birkhoff-Witt Theorem for profinite pronilpotent Lie algebras in which their symmetric and universal enveloping algebras are replaced with appropriate formal analogues and discuss some immediate corollaries of this result.

Original language | English |
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Pages (from-to) | 611-618 |

Number of pages | 8 |

Journal | Journal of Lie Theory |

Volume | 29 |

Issue number | 3 |

State | Published - 2019 |

### Keywords

- Formal power series
- Infinite-dimensional Lie algebra
- Poincaré-Birkhoff-Witt
- Profinite vector space
- Pronilpotent Lie algebra

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## Cite this

Hamilton, A. (2019). A Poincaré-Birkhoff-Witt theorem for profinite pronilpotent Lie algebras.

*Journal of Lie Theory*,*29*(3), 611-618.