  We compute the (1,1)-Aeppli cohomology of compact simply-connected Lie
groups. From this, we deduce that the Bismut flat metrics on the compact Bismut
flat manifolds with finite fundamental group are globally stable for the
pluriclosed flow. This prevents the existence of non-flat homogeneous Bismut
Hermitian Einstein (hence also pluriclosed Calabi--Yau with torsion) metrics on
C-spaces.
