The cohomologies of the Iwasawa manifold and of its small deformations

We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure. We use these tools to compute the Bott–Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, completing the computations by M. Schweitzer (arXiv:​0709.​3528v1 [math.AG]).