## Adjoint operators in Lie algebras and the classification of simple flexible Lie-admissible algebras

Let H be a finite-dimensional flexible Lie-admissible algegra over an algebraically closed field F of characteristic 0. It is shown that if H/sup -/ is a simple Lie algegra which is not of type A/sub n/ (n greater than or equal to 2) then H is a Lie algebra isomorphic to H/sup -/, and if H/sup -/ is a simple Lie algebra of type A/sub n/ (n greater than or equal to 2) then H is either a Lie algebra or isomorphic to an algebra with multiplication x not equal to y = ..mu..xy + (1 - ..mu..)yx - (1/(nmore »