Inhomogeneous hypercomplex structures on homogeneous manifolds

We study deformations of hypercomplex structures on compact homogeneous spa ces through the complex deformation theory of the associated twister spaces . In general, we find complete parameter spaces of hypercomplex structures associated to compact semi-simple Lie groups. In particular, we discover th e moduli space of hypercomplex structures on products of Hopf surfaces and on compact associated bundles of quaternionic projective spaces.