Classification of Simple Lie Algebras on a Lattice

Kenji Iohara, Olivier Mathieu

Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra $\mathcal{L}={\oplus }_{\lambda \in \Lambda }{\mathcal{L}}_{\lambda }$ such that $\dim {\mathcal{L}}_{\lambda }=1$ for all $\lambda$. In this articl…