LiePy

A python package for computations in Lie theory.

There are three main classes:

• RootSystem
• DynkinDiagram
• CartanMatrix

And there are functions to go from one to the other.

This was originally created to do computations for this paper (see Section 6). [arxiv link]

Examples

For example, the following snippet prints the LaTeX code for the Hasse diagram of the poset of root subsystems of the symplectic Lie algebra sp(8, C) (i.e. type C4)

import liepy

# Create Dynkin diagram object for the Lie algebra sp(8, C)
dynkin = liepy.DynkinDiagram('C4')

# Create the corresponding root system
rootsystem = liepy.RootSystem(dynkin)

# Compute the poset of root subsystems.
poset = rootsystem.poset_subsystems()

# Output the LaTeX code
poset.latex_hasse()

Which gives

Similarly, we can do this for the exceptional Lie algebra F4, which gives:

See the paper for more examples.