We continue the investigation of
the simple anti-commutative algebras obtained from a homogeneous general L.t.s. In
particular we consider the algebra which satisfies
(1)
The usual process of analyzing a nonassociative algebra is to decompose it relative
to elements whose right and left multiplications are diagonalizable linear
transformations e.g. idempotents or Cartan subalgebras. In this paper we show that
such a process yields only Lie algebras and indicates the difficulty in finding any
non-Lie multiplication table for a simple anticommutative algebra satisfying
(1).
