Classification of Simple Lie Algebras on a Lattice

Abstract

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 article, we classify all simple graded Lie algebras on a lattice.

Cited by in corpus (2)

• Transposed Poisson structures on Witt type algebras
• Classification of Simple Cuspidal Modules over a Lattice Lie Algebra of Witt type