Documentation	Source	Citation

This package is a rework of the Lie group features of Manifolds.jl in a unified way into a separate package. It especially puts more focus on the Lie group defaults and handling the corresponding Lie algebra.

Installation

In Julia you can install this package by typing

using Pkg; Pkg.add("LieGroups")

in the Julia REPL. For a first start, see the get started tutorial.

You can also watch an introduction given at JuliaCon 2025

or look at the slides from the presentation here.

Contributing

Contributions are encouraged and appreciated! See the Contributing page in the documentation for further notes, for example the code style.

Citation

If you use LieGroups.jl in your work, please cite the following open access JuliaCon proceedings paper

@article{BergmannBaran:2026,
    Author = {Bergmann, Ronny and Baran, Mateusz},
    Doi = {10.21105/jcon.00195},
    Journal = {Proceedings of the JuliaCon Conferences},
    Volume = {8},
    Number = {79},
    Pages = {195}, Year = {2026},
    Publisher = {The Open Journal},
    Title = {Groups and smooth geometry using LieGroups.jl},
}

To refer to a certain version, we recommend to also cite for example

@software{axen_2025_17737448,
  Author = {Axen, Seth D. and Baran, Mateusz and Bergmann, Ronny and Tu, Yueh-Hua and Verdier, Olivier},
  Doi = {10.5281/zenodo.15343362},
  Publisher    = {Zenodo},
  Title        = {LieGroups.jl},
  Year         = {2025},
}

for the most recent version or a corresponding version specific DOI, see the list of all versions. Note that both citations are in BibLaTeX format.

Note

This is a rework of the features from Manifolds.jl. See transition from Manifolds.jl for a comprehensive list how to update your code. This especially also includes a few different choices in default behaviour that is different from the Manifolds.jl one. For purely manifold-based operations, any Lie group still is “build upon” a Riemannian manifold.