Kenji Iohara, Olivier Mathieu
Published 2011-07-11, updated 2012-04-03Version 2
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.
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