4 papers
Metric equivalences of Heintze groups and applications to classifications in low dimension
Ville Kivioja, Enrico Le Donne, Sebastiano Nicolussi Golo
We approach the quasi-isometric classification questions on Lie groups by considering low dimensional cases and isometries alongside quasi-isometries. First, we present some new re…
Gradings for nilpotent Lie algebras
Eero Hakavuori, Ville Kivioja, Terhi Moisala +1
We present a constructive approach to torsion-free gradings of Lie algebras. Our main result is the computation of a maximal grading. Given a Lie algebra, using its maximal grading…
From homogeneous metric spaces to Lie groups
Michael G. Cowling, Ville Kivioja, Enrico Le Donne +2
We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively. After a review of some classical results, we u…
Isometries of nilpotent metric groups
Ville Kivioja, Enrico Le Donne
We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object met…