Some Generalized Kac-Moody Algebras With Known Root Multiplicities
نویسنده
چکیده
Starting from Borcherds’ fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including AE3.
منابع مشابه
On Root Multiplicities of Some Hyperbolic Kac-Moody Algebras
Using the coset construction, we compute the root multiplicities at level three for some hyperbolic Kac-Moody algebras including the basic hyperbolic extension of A (1) 1 and E10. Member of the CNRS Laboratoire de la Direction des Sciences de la Matière du Commisariat à l’Energie Atomique.
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