Is there a Lie type algebra on the Leech lattice?

Question

Lattices such as the $E_8$ lattice can be made into a Lie Algbera.

The $E_8$ lattice is the densest packing of spheres in 8D. In 24D this is the Leech lattice $\Lambda_{24}$.

Is there any kind of algebra associated with the Leech Lattice (even if it is not a Lie algebra?)

Answer 1

There is an vertex operator algebra of the Leech lattice, see for example this article here. For more information on how to construct vertex operator algebras using lattices, see this MO-question.