Seminar "Geometric structures on manifolds": Yulia Gorginyan's pre-defense talk

A hypercomplex structure on a Lie algebra is a triple of complex structures I, J, and K satisfying the quaternionic relations. A quaternionic-solvable Lie algebra is a Lie algebra, admitting a finite filtration by quaternionic-invariant subalgebras, such that each successive quotient is abelian.
We will discuss the quaternionic-solvable hypercomplex structures on a nilpotent Lie algebra and hypercomplex nilmanifolds, corresponding to them.