Lie Algebras with Prescribed sl3 Decomposition
Rings and Algebras
2011-03-10 v2
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.
Cite
@article{arxiv.1101.0489,
title = {Lie Algebras with Prescribed sl3 Decomposition},
author = {Georgia Benkart and Alberto Elduque},
journal= {arXiv preprint arXiv:1101.0489},
year = {2011}
}
Comments
13 pages. Minor changes over the first version. To appear in Proc. Amer. Math. Soc