Einstein metrics on compact Lie groups which are not naturally reductive

The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by D’Atri and Ziller (Mem Am Math Soc 18, (215) 1979). In 1996 the second author obtained non-naturally reductive Einstein metrics on the Lie group SU(n) for n ≥  6, by using a method of Riemannian submersions. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) (n ≥  11), Sp(n) (n ≥  3), E6, E7, and E8.