CLASSIFICATION OF SIMPLE LIE ALGEBRAS ON A LATTICE

Kenji Iohara (1) , Olivier Mathieu (2)

1 ICJ - Institut Camille Jordan
2 AGL - Algèbre, géométrie, logique

Let $\Lambda$ be a lattice of rank $n$. In this article, we classify all $\Lambda$-graded Lie algebras ${\cal L}=\bigoplus_{\lambda \in \Lambda}{\cal L}_\lambda$ such that ${\cal L}$ is simple-graded and that $\dim {\cal L}_\lambda=1$ for all $\lambda \in \Lambda$.

Domaines: Théorie des représentations [math.RT]

Kenji Iohara, Olivier Mathieu. CLASSIFICATION OF SIMPLE LIE ALGEBRAS ON A LATTICE. Proceeding of the London Mathematical Society, 2013, 106 (3), pp.508 -- 564. ⟨10.1112/plms/pds042⟩. ⟨hal-00608430⟩