Timeline for Is the Cartan matrix a complete invariant of a Kac-Moody algebra?
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| Feb 25, 2010 at 12:31 | comment | added | user717 | Ah, and if A is a symmetrizable Cartan matrix, then it follows from a theorem by Gabber-Kac that g(A) has a presentation like finite-dimensional semisimple lie algebras, i.e. Serre relations and stuff. | |
| Feb 25, 2010 at 12:29 | comment | added | user717 | I think so. Kac gives a general construction of a Lie algebra g(A) for a complex matrix A. If A is a (generalized) Cartan matrix, then he calls g(A) a Kac-Moody algebra. Cartan matrices of finite and affine type are symmetrizable, so here everything is okay. But I don't think this holds for Cartan matrices of indefinite type... | |
| Feb 25, 2010 at 12:23 | comment | added | José Figueroa-O'Farrill | Do non-symmetrisable Cartan matrices also give rise to Kac-Moody algebras? i.e., does the construction in terms of Serre relations still go through? And what sort of Lie algebra do you get? Sorry, this seems like a question, more than a comment... I'm just curious. | |
| Feb 25, 2010 at 10:29 | history | asked | user717 | CC BY-SA 2.5 |