Positive Hermitian curvature flow on nilpotent and almost-abelian complex Lie groups

We study the positive Hermitian curvature flow on space of left-invariant metrics complex Lie groups. show that in nilpotent case, exists for all times and subconverges Cheeger-Gromov sense to a soliton. also convergence soliton when group is almost abelian. That is, its algebra admits (complex) co-dimension one abelian ideal. Finally, we solitons almost-abelian setting. prove uniqueness completely classify left-invariant, solitons, giving method construct examples arbitrary dimensions, many which admit co-compact lattices.