Abstract
We investigate to what extent a nilpotent Lie group is determined by its [Formula: see text]-algebra. We prove that, within the class of exponential Lie groups, direct products of Heisenberg groups with abelian Lie groups are uniquely determined even by their unitary dual, while nilpotent Lie groups of dimension [Formula: see text] are uniquely determined by the Morita equivalence class of their [Formula: see text]-algebras. We also find that this last property is shared by the filiform Lie groups and by the [Formula: see text]-dimensional free two-step nilpotent Lie group.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
