Lattice vertex algebras on general even, self-dual lattices
نویسنده
چکیده
In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Γ with p ≥ q. It is known that if the lattice is of rank ≤ 26 and 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 > 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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