Hello all,
I've been working on and thinking about my proposal for a Lie Algebra
module. Ideally I'd like to have the following classes:
- Cartan Type (eg A4, B3, etc)
- subclasses would implement Dynkin diagrams and the Cartan matrix
- also include functions to return the rank of the given Lie algebra,
and whether or not it is finite
- Weyl group
- This would return the Weyl group of a given classical Lie algebra,
as well as be able to return the simple reflections
- RootSystem
- Output the root system of a given Cartan type
- Keep the roots either in a dictionary or an array to allow the user
to perform operations with the roots
I'd also like to have files with the basic information about for the
different classical Lie algebras (A,B,C,D,E,F,G). One source that is
particularly useful is Lie Algebras: Theory and Algorithm by W.A. de
Graaf. I also own several other books on Weyl groups and Lie algebras in
general that I think would be quite useful for this project.
I was hoping others could provide feedback on what I have so far for this
project!
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