Timeline for Matrices of Lie algebra of Dynkin diagram B2 [closed]
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 20, 2023 at 18:41 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title, while this is on the front page; does not resolve close reason
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| Jan 31, 2011 at 3:19 | history | closed | S. Carnahan♦ | no longer relevant | |
| Jan 17, 2011 at 18:13 | comment | added | garretstar | Thanks, I have found this answer helpful. Also, I have just discovered the book, "Notes on Lie Algebras" by Hans Samelson, which has clarified the issue. | |
| Jan 17, 2011 at 18:09 | vote | accept | garretstar | ||
| Jan 17, 2011 at 18:09 | |||||
| Jan 17, 2011 at 6:54 | comment | added | José Figueroa-O'Farrill | @Guntram: that's also not a research-level question, Allen's answer notwithstanding. See his answer for how to go about it. In any case, you don't get this from the Cartan matrix. | |
| Jan 17, 2011 at 1:06 | answer | added | Allen Knutson | timeline score: 3 | |
| Jan 16, 2011 at 21:26 | comment | added | Guntram | The question is: what are the matrices corresponding to the Chevalley generators, i.e. the famous (e_i,f_i,h_i)? | |
| Jan 16, 2011 at 20:28 | comment | added | José Figueroa-O'Farrill | I am not sure I understand this question. Why would you expect the Cartan matrix to give you a particular matrix representation? The Cartan matrix gives you the structure of the Lie algebra using the Serre relations. This is explained in a variety of places, e.g., Humphrey's book on Lie algebras and representation theory. $$ $$ The compact real form of the Lie algebra of type B2 is the algebra of skewsymmetric endomorphisms of a five-dimensional euclidean space. It doesn't get any more explicit than that: just take the 5x5 skewsymmetric matrices. | |
| Jan 16, 2011 at 19:33 | history | asked | garretstar | CC BY-SA 2.5 |