Lie

A numerical library for working with (representations) of Lie Groups and Algebras.

Features

• [x] Spin matrices su(2) and ladder matrices sl(2, C)
• [x] Generalized Gell-Mann Matrices su(n) (Hermitian)
• [x] [Sylverster](https://en.wikipedia.org/wiki/GeneralizedCliffordalgebra) "Clock" and "Shift" Matrices su(n) (non-Hermitian)
• [x] su(n) matrices by "Spherical Harmonics Tensors su(2) addition" via Clebsh-Gordan coefficients
• [x] Computation of Structure constants
• [x] Computation of dot/cross product in su(n) through structure constants

Examples

Python bindings

python import liepy as lp su_algebra = lp.gen_gellmann(3) Additional examples, and notebooks, can found here.

Rust

```rust use lie::gellmann::; use lie::lie_algebra::; let sualgebra = getgellmann(3); let f = findstructureconstants(su_algebra);

println!("{:?}", f); ```

Installation

Pre-built binary wheels are available.

pip install liepy

Compiling from source

Lie depends on:

• openblas-devel, e.g. (for Ubuntu/Debian sudo apt install libopenblas-devel) or equivalent
• Rust >= 1.58
• Maturin

git clone https://github.com/RustyBamboo/lie cd lie/liepy maturin build --release --manylinux=off pip3 install target/wheels/liepy-....whl --force-reinstall

Building for manylinux

For manylinux compiled wheel, a Docker container is used.

cd lie docker build -t maturin liepy/ docker run --rm -v $(pwd):/io maturin build --release -m liepy/Cargo.toml

Tests

To ensure the library is working as intended, a test can be run:

cargo test

License

Lie is free and opensource, released under MIT license.