Classification of Simple Lie Algebras on a Lattice
  Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$ for all $\lambda$. In this article, we classify all simple graded Lie algebras on a lattice. 
Kenji Iohara and Olivier Mathieu
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