On classification of Lorentzian Kac-Moody algebras
By V. Gritsenko, V. Nikulin. 2002
48 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/877414a34b6df954c2012655b54272c37dea7cbb
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In Geometry and Topology
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Citations in the corpus
- Reflection groups in algebraic geometry (2006, unknown): “Nikulin on Lorentzian Kac-Moody algebras [52].”
- On the classification of automorphic products and generalized Kac–Moody algebras (2006, methodology): “Our definitions of reflective forms are motivated by Borcherds’ definition of reflective scalar valued modular forms in [B4] and Gritsenko and Nikulin’s definition of reflective automorphic forms in [ GN ].”