Depth Generated Simple Lie Algebras

A Lie module algebra for a Lie algebra L is an algebra and L-module A such that L acts on A by derivations. The depth Lie algebra [inline-graphic not available: see fulltext] of a Lie algebra L with Lie module algebra A acts on a corresponding depth Lie module algebra [inline-graphic not available: see fulltext]. This determines a depth functor [inline-graphic not available: see fulltext] from the category of Lie module algebra pairs to itself. Remarkably, this functor preserves central simplicity. It follows that the Lie algebras [inline-graphic not available: see fulltext] corresponding to faithful central simple Lie module algebra pairs (A,L) with A commutative are simple. Upon iteration at such (A,L), the Lie algebras [inline-graphic not available: see fulltext] are simple for all i ∈ ω. In particular, the [inline-graphic not available: see fulltext] (i ∈ ω) corresponding to central simple Jordan Lie algops (A,L) are simple Lie algebras.