Lie Algebras with Prescribed sl3 Decomposition

Details Lie Algebras with Prescribed sl3 Decomposition Lie Algebras with Prescribed sl3 Decomposition

2011-01-03

arxiv.org/abs/1101.0489v2

Mathematics

Rings and Algebras

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

Scientific paper

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.

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