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We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, \(RCD^*(K,N),\) 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.

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