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Lattice Vertex Algebras on General Even, Self-dual Lattices

Axel Kleinschmidt
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Abstract

In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Gamma^{p,q} with p greater or equal to q. It is known that if the lattice is at most Lorentzian, the resulting Lie algebra is of generalized Kac-Moody type (or has a quotient that is). We show that this is not true as soon as q is larger than 1. By studying a certain sublattice in the case q>1 we obtain results that lead to the conjecture that the resulting non-GKM Lie algebra cannot be described conveniently in terms of generators and relations and belongs to a new and qualitatively different class of Lie algebras.

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Axel Kleinschmidt. 2003-02-11. Lattice Vertex Algebras on General Even, Self-dual Lattices. https://doi.org/10.1088/1126-6708%2F2003%2F07%2F069

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