Non-naturally reductive Einstein metrics on exceptional Lie groups (Q2400293)

Let \(G\) be an exceptional compact simple Lie group. The authors introduce a new left-invariant Einstein metrics (not naturally reductive). For the exceptional Lie group \(G_2\) the first known example of a left-invariant Einstein metric is constructed. For the Lie groups \(E_7\) and \(E_8\), the authors prove that there exist non-isometric non-naturally reductive Einstein metrics, which are \(\mathrm{Ad}(K)\)-invariant by some Lie subgroups \(K\).