Published online by Cambridge University Press: 20 November 2018
In this note we give a correction to the proof of the following theorem [1, Theorem 2].
THEOREM. Letbe a flexible, power-associative algebra, over an arbitrary algebraically closed field Ω of characteristic 0. If
is a simple Lie algebra, then
is a simple Lie algebra isomorphic to
.
Step (i) of the proof, which proves that the Cartan subalgebra of
is a nil subalgebra of
, is incomplete. Assuming that
is not a nil subalgebra of
, there exists an idempotent e ≠ 0 in
.