On Tue, Feb 10, 2009 at 6:28 PM, Greg Kuperberg <[email protected]> wrote: > > For a certain reason, I am interested in the Lie algebra generated by > the generators of the Temperley-Lieb algebra, in its natural Catalan- > dimensional representation. In other words given the T-L algebra with > 2n strands, I am looking at a C_n x C_n matrix algebra quotient, where > C_n is the nth Catalan number. Then in this quotient, the 2n-1 > Temperley-Lieb generators also generate a Lie algebra. I only need 8 > strands for the problem that I am studying. Thus it's a question in > 14 x 14 matrices. > > I wrote a SAGE/Python program to compute the matrices of the Temperley- > Lieb generators, and then I gave them to GAP from SAGE. It isn't all > that fast, because GAP does not use the fact that the matrices are > sparse, but it works. Sort of. The problem is that the Temperley- > Lieb algebra has a parameter d, and I want to know the answer for all > d. My code can give me the answer for a specific d working over QQ. > But if I want the answer for all d, I should be working over the > polynomial ring QQ[d]. > > Note that it is not hard to rephrase the question as a module question > in R^(14^2), where R is the ground ring. I can write down the Lie > adjoint action of the Temperley-Lieb generators on 14 x 14 matrices > expressed as vectors. I can generate an invariant submodule, and I am > then interested in the Smith Normal Form of this submodule, or > equivalently the isomorphism type of the quotient module. I have to > think a bit about keeping the number of generators of the module under > control, but maybe there is a way. > > My impression is that both GAP and SAGE can easily understand the > question when it is posed over a field, but not over a univariate > polynomial ring as I actually want. Am I wrong and is there a > reasonable way to do this?
David Loeffer recently added computation of Smith Normal Forms over more general rings to Sage. See: http://trac.sagemath.org/sage_trac/ticket/4681 William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
