On the isometry group of $RCD^*(K,N)$-spaces
  We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RCD^*(K,N),$ is in fact a Lie group. We obtain an optimal upper bound on its dimension and classify the spaces where this maximal dimension is achieved. 
Luis Guijarro and Jaime Santos-Rodr\'iguez
math.DG math.MG