On Locally Symmetric $3$-Dimensional Riemannian Lie Groups
  In this paper, we use the powerful tool Milnor bases to classify all the $3-$dimensional connected and locally symmetric Riemannian Lie Groups by solving system of polynomial equations of structure constants of each Lie algebra . Moreover, we showed that $E_0(2)$, is the only Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric. 
Nimpa Pefoukeu Romain (nimpapefoukeu@yahoo.fr), Wouafo Kamga Jean   (wouafoka@yahoo.fr), Djiadeu Ngaha Michel Bertrand (djia...
math.DG