Abstract
The general theory of Lorentzian Kac-Moody algebras is considered. This theory must serve as a hyperbolic analogue of the classical theories of finite-dimensional semisimple Lie algebras and affine Kac-Moody algebras. The first examples of Lorentzian Kac-Moody algebras were found by Borcherds. Here general finiteness results for the set of Lorentzian Kac-Moody algebras of rank ≥3 are considered along with the classification problem for these algebras. As an example, a classification is given for Lorentzian Kac-Moody algebras of rank 3 with hyperbolic root lattice , symmetry lattice , and symmetry group , , where and are given by and is trivial on , is the extended paramodular group. This is perhaps the first example in which a large class of Lorentzian Kac-Moody algebras has been classified.
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