  In our investigation on quantum gravity, we introduce an infinite dimensional
complex Lie algebra $\textbf{${\mathfrak g}_{\mathsf u}$}$ that extends
$\mathbf{e_9}$. It is defined through a symmetric Cartan matrix of a rank 12
Borcherds algebra. We turn $\textbf{${\mathfrak g}_{\mathsf u}$}$ into a Lie
superalgebra $\textbf{$\mathfrak {sg}_{\mathsf u}$}$ with no superpartners, in
order to comply with the Pauli exclusion principle. There is a natural action
of the Poincar\'e group on $\textbf{$\mathfrak {sg}_{\mathsf u}$}$, which is an
automorphism in the massive sector. We introduce a mechanism for scattering
that includes decays as particular {\it resonant scattering}. Finally, we
complete the model by merging the local $\textbf{$\mathfrak {sg}_{\mathsf u}$}$
into a vertex-type algebra.
