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.
LieGroups.jl is a new package in the 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.
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 interface
- generic interfaces for both group operations and group actions
- several Meta-Lie groups, especially a generic approach to define semidirect product groups including an ovealoaded \ltimes operator
- a library of Lie groups covering among others
There will also be a talk at the JuliaCon this year about this package, see here, as well as an overview talk about JuliaManifolds.
We hope this is useful to anyone working with Lie groups and would love to hearfeedback and further ideas that could be covered.