%0 Journal Article %T Non-naturally reductive Einstein metrics on the compact simple Lie group $F_4$ %A Zhiqi Chen %A Ke Liang %J Mathematics %D 2013 %I arXiv %X Based on the representation theory and the study on the involutions of compact simple Lie groups, we show that $F_4$ admits non-naturally reductive Einstein metrics. %U http://arxiv.org/abs/1311.5288v1