Biggs, RoryNtshudisane, Odirile2023-09-012023-09-012024Biggs, R. & Ntshudisane, O.K.L. 2024, 'On the classification of sub-Riemannian structures on a 5D two-step nilpotent Lie group', Communications in Mathematics, vol. 32, no. 1, pp. 13-22, doi : 10.46298/cm.10550.2336-1298 (online)1804-1388 (print)10.46298/cm.10550http://hdl.handle.net/2263/92134We 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).enArticle is published under Licence: Attribution 4.0 International (CC BY 4.0).Two-step nilpotent Lie groupIsometriesSub-Riemannian structureArticle