10th May 2004 - 07:09 PM
stainless steel T 304,
what the T means?
19th January 2012 - 08:33 AM
Do you think I should have spoken about n generators? I really haven't internalized most of Lang's Algebra or all of Georgi's Lie Algebras in Particle Physics. Neither of which tackles general Lie algebras in depth....
Well, obviously a lot of education separates us, so it very well might be that I am confused. But my original thought was that should hold for any Lie algebra, with implying , implying and the Jacobi identity giving us additional constraints on the remaining unknown elements of . I'm aware that the general Lie algebra could be over some finite field or space of rational functions, but I assumed that we were talking complex numbers. (The choice of K seems to be a poor one, now that I have seen the draft paper, but I didn't want to use the convention of Georgi, , which conviniently results in real f when the algebra is unitary. So lets drop K in favor of f. ) But since I was under the impression that that it should be possible to automate solution over a small number of algebraic numbers of low degree. (I'm not saying give it to Mathematica's Solve, but write custom software to help explore it, and ideally solve it completely. Solve is impressive but when it fails or takes to you get no closer to a solution. Also, I don't have it. )
Since then, I have realized that does not imply that any of a,b,c or d is algebraic, but it still branchs into two cases: or and with so many more equations than unknowns, I thought computer methods had real potential, even if I can't prove that. (That's the type of identification of cases and small theorems that remind me of sudoku.)
I think that additional information like the isometries and equation 8.1 from the draft paper just makes things easier. But, as I'm still struggling to read the paper and have not been able to set up the problem in a form which is entirely comphrehensible for myself. For example, I don't know how to express my 792 unknowns in terms of AlphaNumeric's 40 unknowns. And I didn't know the result AlphaNumber quotes where [a,b] = c is the same algebra as [a,b] = 2c.
I'm not disagreeing with Guest254 that this is a daunting problem whose solution would be worthy of a paper of its own. I'm just interested in exploring of how to get man and machine to work together on this problem. Sorry if I've damaged myself in your view. One never feels so stupid as when one is learning.