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

Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow