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There are 10 generalized Kac-Moody algebras whose denominator identities arecompletely reflective automorphic products of singular weight on lattices ofsquarefree level. Under the assumption that the meromorphic vertex operatoralgebra of central charge 24 and spin-1 algebra $\hat{A}_{p-1,p}^r$ exists weshow that four of them can be constructed in a uniform way from bosonic stringsmoving on suitable target spaces.

Natural constructions of some generalized Kac-Moody algebras as bosonic strings