On the isometry group of $$RCD^*(K,N)$$RCD∗(K,N)-spaces

Abstract

We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $$RCD^*(K,N),$$RCD∗(K,N), is a Lie group. We obtain an optimal upper bound on the dimension of this group, and classify the spaces where this maximal dimension is attained.