  We introduce a quantum model for the Universe at its early stages,
formulating a mechanism for the expansion of space and matter from a quantum
initial condition, with particle interactions and creation driven by algebraic
extensions of the Kac-Moody Lie algebra $\mathbf{e_9}$. We investigate
Kac-Moody and Borcherds algebras, and we propose a generalization that meets
further requirements that we regard as fundamental in quantum gravity.
