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Abstract Borcherds-Kac-Moody algebras are natural generalisations of finite-dimensional simple Lie algebras. There are exactly 10 Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of squarefree level (classified by Scheithauer). These belong to a larger class of Borcherds-Kac-Moody (super)algebras obtained by Borcherds by twisting the denominator identity of the Fake Monster Lie algebra. For the 10 Lie algebras we prove a conjecture by Borcherds that they can be realised uniformly as the physical states of bosonic strings moving on suitable spacetimes. This amounts to applying the BRST formalism to certain vertex algebras of central charge 26 obtained as graded tensor products of abelian intertwining algebras.

Zoom link https://rutgers.zoom.us/j/93921465287
Meeting ID: 939 2146 5287
Passcode: 196884, the dimension of the weight 2 homogeneous
subspace of the moonshine module