Lie Algebras with Prescribed sl3 Decomposition

Abstract

In this work, we consider Lie algebras L containing a subalgebra isomorphic to sl3 and such that L decomposes as a module for that sl3 subalgebra into copies of the adjoint module, the natural 3-dimensional module and its dual, and the trivial one-dimensional module. We determine the multiplication in L and establish connections with structurable algebras by exploiting symmetry relative to the symmetric group S4.

arXiv comment13 pages. Minor changes over the first version. To appear in Proc. Amer. Math. Soc