  An operator $I$ on a real Lie algebra $A$ is called a complex structure
operator if $I^2=-Id$ and the $\sqrt{-1}$-eigenspace $A^{1,0}$ is a Lie
subalgebra in the complexification of $A$. A hypercomplex structure on a Lie
algebra $A$ is a triple of complex structures $I,J$ and $K$ on $A$ satisfying
the quaternionic relations. We call a hypercomplex nilpotent Lie algebra
quaternionic-solvable if there exists a finite filtration by
quaternionic-invariant subalgebras with commutative subquotients which
converges to zero. We give examples of quaternionic-solvable hypercomplex
structures on a nilpotent Lie algebra and conjecture that all hypercomplex
structures on nilpotent Lie algebras are quaternionic-solvable. Let $(N,I,J,K)$
be a compact hypercomplex nilmanifold associated to an quaternionic-solvable
hypercomplex Lie algebra. We prove that, for a general complex structure $L$
induced by quaternions, there are no complex curves in a complex manifold
$(N,L)$.
