A couple of questions: How would you represent the Weyl gp? As a permutation group? How would you represent an element of a root system? As both a dict or a vector (or just one or the other)? Would you implement a group action on the root lattice? Would you implement a Lie algebra as a vector space over QQ with a bracket operation? If not, how?
On Thu, Apr 4, 2013 at 7:37 PM, Mary Clark <[email protected]>wrote: > 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! > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy?hl=en-US. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy?hl=en-US. For more options, visit https://groups.google.com/groups/opt_out.
