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Let 31 be a finite-dimensional flexible Lie-admissible algebra over an algebraically closed field F of characteristic 0. It is shown that if 21 ~ is a simple Lie algebra which is not of type An (n > 2) then 21 is a Lie algebra isomorphic to 21", and if 9t is a simple Lie algebra of type An (n > 2) then 21 is either a Lie algebra or isomorphic to an algebra with multiplication x » y = pxy + ( 1 -¡i)yx -(l/(n + l))Tr(xy)/ which is defined on the space of (n + 1) X (n + 1) traceless matrices overdoi:10.1090/s0002-9947-1981-0603775-4 fatcat:56chctj77bcgheutlkcgaohlem