Abstract:
We classify the left-invariant sub-Riemannian structures on the unique
five-dimensional simply connected two-step nilpotent Lie group with two-dimensional
commutator subgroup; this 5D group is the first two-step nilpotent Lie group beyond
the three- and five-dimensional Heisenberg groups. Alongside, we also present a
classification, up to automorphism, of the subspaces of the associated Lie algebra
(together with a complete set of invariants).
