Is $SL(n,F)$ a Kac-Moody group? Do Kac-Moody groups generalize the classical Lie groups or are they a different family of groups?
I can't find an exposition of the material that I can understand, and really I'm just looking for a yes/no answer. A Kac-Moody algebra seems to be a generalization of the classical Lie algebras, as a classical Lie algebra could be described by a generalize Cartan matrix, since this is (obviously) just a generalization of a Cartan matrix.
Sorry if this is a dumb question...
Every finite-dimensional semisimple Lie algebra is a Kac-Moody algebra and so every finite-dimensional semisimple Lie group is a Kac-Moody group (assuming "Kac-Moody group" means what I think it means, namely "a group whose Lie algebra is a Kac-Moody algebra"). But it's a bit like "every square is a rectangle"; in practice if someone's writing a paper about Kac-Moody groups or algebras they are studying the infinite-dimensional case.