This package provides basic implementation of arbitrary finite-dimensional Lie algebras for the free and open source SymPy computer algebra system. It features:
- definition of Lie algebras by their basis and defining Lie bracket operation on basis elements,
- calculating the Lie bracket on elements of Lie algebras,
- subalgebras,
- product ideals,
- lower central series and derived series,
- adjoint representations,
- solvable radical,
- nilradical,
- Levi decomposition,
- universal enveloping algebras and basic operations within them
Make sure you have installed the Sympy package for your Python environment. You can do so by executing:
pip install --user sympy
All you have to do now is to download and unpack this repository. Import the LieAlgebra class from the LieAlgebra.py file and you are ready to start your computations.
Overview of files and documentation of the package can be found in the wiki page of the project.
Feel free to contact me if you want to give any feedback, point out bugs or mistakes, etc. The project is licensed under GNU GPLv3 license.