Timeline for "isotropic" subspaces of a simple Lie algebra
Current License: CC BY-SA 2.5
4 events
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| Nov 1, 2009 at 6:52 | comment | added | José Figueroa-O'Farrill | Thanks. I have several comments. First of all, any two-dimensional subspace is automatically isotropic, since the isotropy condition is with respect to a 3-form. The question is, though, if they are maximally isotropic. My second comment is that the two matrices which you suggest, are not in su(3). For one thing, they are real and symmetric. Perhaps you meant changing the signs on the entries below the diagonal, which makes them skewsymmetric and hence in su(3). But in this case, I think that this subspace is not maximally isotropic in su(3). | |
| Oct 31, 2009 at 14:15 | comment | added | David Bar Moshe | I meant upper and lower second and third diagonals. The nonvanishing terms in the first generator are a_{i, i+1} and a{i,i-1} which are ones and all other entries zero. Similarly the second generator consists of ones in the entries a{i, i+2} and a{i, i-2}. | |
| Oct 31, 2009 at 13:19 | comment | added | José Figueroa-O'Farrill | I am afraid I do not understand what you mean by "(+-) second and third diagonals". In the notation where a_{ij} denotes the entry of the matrix a on the i-th row and j-th column, could you tell me which entries are nonzero? Thanks. | |
| Oct 31, 2009 at 5:14 | history | answered | David Bar Moshe | CC BY-SA 2.5 |