  We compute the (1,1)-Aeppli cohomology of compact simply-connected simple Lie
groups of rank two. In particular, we verify that they are of dimension one and
generated by the classes of the Bismut flat metrics coming from the Killing
forms. This yields a result on the stability of the pluriclosed flow on these
manifolds. Moreover, we show that for compact simply-connected simple Lie
groups of rank two the Dolbeaut cohomology, as well as the Bott-Chern and the
Aeppli cohomologies, arise from just the left-invariant forms and we computed
the whole Bott-Chern diamonds of SU(3) and Spin(5) when they are equipped with
a left-invariant isotropic complex structure.
