# \[ANN\] LieGroups.jl

**URL:** <https://discourse.julialang.org/t/ann-liegroups-jl/128294>\
**Category:** Package Announcements\
**Created:** [April 22, 2025, 11:24am UTC](https://discourse.julialang.org/t/ann-liegroups-jl/128294 "2025-04-22T11:24:36Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![kellertuer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kellertuer/32/220707_2.png) [@kellertuer](https://discourse.julialang.org/u/kellertuer)\
**Post date:** [April 22, 2025, 11:24am UTC](https://discourse.julialang.org/t/ann-liegroups-jl/128294/1 "2025-04-22T11:24:36Z")

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Lie groups are a tool to work with groups, namely they are a manifold equipped with a smooth group operation. In practice these appear when dealing with rotations on a Euclidean space, the set of translations and rotations, or so-called symplectic matrices in Hamiltonian systems.

 ![logo with text](https://global.discourse-cdn.com/julialang/original/3X/8/9/890e1d9f1442a9b470629b3b39c41409be50b24b.png)

[LieGroups.jl](https://github.com/JuliaManifolds/LieGroups.jl) is a new package in the [Juliamanifolds](https://github.com/JuliaManifolds) ecosystem and provides both an interface to work with and define Lie groups as well as a library of Lie groups.  
These are built on the manifolds defined in [Manifolds.jl](https://github.com/JuliaManifolds/Manifolds.jl).  
While Manifolds.jl contains a predecessor, the `GroupManifolds` approach to Lie groups, the new package puts an even stronger focus on Lie group features.

Main features of this new package are:

- a generic [LieAlgebra](https://juliamanifolds.github.io/LieGroups.jl/stable/interface/algebra/) interface
- generic interfaces for both [group operations](https://juliamanifolds.github.io/LieGroups.jl/stable/interface/operations/) and [group actions](https://juliamanifolds.github.io/LieGroups.jl/stable/interface/actions/)
- several Meta-Lie groups, especially a generic approach to define [semidirect product groups](https://juliamanifolds.github.io/LieGroups.jl/stable/groups/semidirect_product_group/) including an ovealoaded \ltimes operator
- a library of Lie groups covering among others
  - the [orthogonal group](https://juliamanifolds.github.io/LieGroups.jl/stable/groups/orthogonal_group/)
  - the [special orthogonal group](https://juliamanifolds.github.io/LieGroups.jl/stable/groups/special_orthogonal_group/)
  - the [special Euclidean group](https://juliamanifolds.github.io/LieGroups.jl/stable/groups/special_euclidean_group/)
  - the [symplectic group](https://juliamanifolds.github.io/LieGroups.jl/stable/groups/symplectic_group/)

There will also be a talk at the JuliaCon this year about this package, see [here](https://pretalx.com/juliacon-2025/talk/JWTZWL/), as well as [an overview talk about JuliaManifolds](https://pretalx.com/juliacon-2025/talk/F98U7E/).

We hope this is useful to anyone working with Lie groups and would love to hearfeedback and further ideas that could be covered.

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<div class="post-metadata">

**Author:** ![kellertuer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kellertuer/32/220707_2.png) [@kellertuer](https://discourse.julialang.org/u/kellertuer)\
**Post date:** [October 9, 2025, 11:36am UTC](https://discourse.julialang.org/t/ann-liegroups-jl/128294/2 "2025-10-09T11:36:45Z")

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# LieGroups.jl 0.1.5

The most recent update from today is just a minor change for LieGroups.jl itself, but concerning the [JuliaManifolds](https://github.com/JuliaManifolds) ecosystem, we could finally remove the (slight) duplication we had between LieGroups.jl and Manifolds.jl s `GroupManifold` structure. Now manifolds with a group structure are all defined and unified in LieGroups.jl. If you used `GroupManifold`s before, check out our detailed [How to transition](https://juliamanifolds.github.io/LieGroups.jl/stable/tutorials/transition/) tutorial and list of changes.

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<div class="post-metadata">

**Author:** ![kellertuer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kellertuer/32/220707_2.png) [@kellertuer](https://discourse.julialang.org/u/kellertuer)\
**Post date:** [December 9, 2025, 6:41am UTC](https://discourse.julialang.org/t/ann-liegroups-jl/128294/3 "2025-12-09T06:41:15Z")

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The talk at JuliaCon was just released on YouTube today, see [https://youtu.be/\_L9u8r42oSQ](https://youtu.be/_L9u8r42oSQ).