Publication details
Non-naturally reductive Einstein metrics on exceptional Lie groups
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Geometry and Physics |
| MU Faculty or unit | |
| Citation | |
| Web | Full Text |
| Doi | http://dx.doi.org/10.1016/j.geomphys.2017.01.030 |
| Keywords | Left-invariant Einstein metrics; Naturally reductive metrics; Exceptional Lie groups; Flag manifolds |
| Description | Given an exceptional compact simple Lie group G we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of G over flag manifolds with a certain kind of isotropy representation and we construct the Einstein equation with respect to the induced left-invariant metrics. Then we apply a technique based on Grobner bases and classify the real solutions of the associated algebraic systems. For the Lie group G(2) we obtain the first known example of a left-invariant Einstein metric, which is not naturally reductive. Moreover, for the Lie groups E-7 and E-8, we conclude that there exist non-isometric non-naturally reductive Einstein metrics, which are Ad(K)-invariant by different Lie subgroups K. |