Le Donne, Enrico; Tripaldi, Francesca (2022). A Cornucopia of Carnot Groups in Low Dimensions. Analysis and geometry in metric spaces, 10(1), pp. 155-289. De Gruyter 10.1515/agms-2022-0138
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Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is homogeneous with respect to the automorphisms induced by the derivation,this metric space is known as Carnot group. Carnot groups appear in several mathematical contexts. To understand their algebraic structure, it is useful to study some examples explicitly. In this work, we provide a list of low-dimensional stratified groups, express their Lie product, and present a basis of left-invariant vector fields, together with their respective left-invariant 1-forms, a basis of right-invariant vector fields, and some other properties. We exhibit all stratified groups in dimension up to 7 and also study some free-nilpotent groups in dimension up to 14.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Tripaldi, Francesca |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
2299-3274 |
Publisher: |
De Gruyter |
Funders: |
[UNSPECIFIED] Academy of Finland grant 288501‘Geometry of subRiemannian groups’ ; [UNSPECIFIED] Academy of Finland grant 322898 ‘Sub-Riemannian Geometry via Metric-geometryand Lie-group Theory’ ; [18] European Research Council ; [UNSPECIFIED] University of Bologna, funds for selected research topics ; [222] Horizon 2020 |
Language: |
English |
Submitter: |
Francesca Tripaldi |
Date Deposited: |
24 Oct 2022 16:08 |
Last Modified: |
05 Dec 2022 16:26 |
Publisher DOI: |
10.1515/agms-2022-0138 |
ArXiv ID: |
2008.12356 |
BORIS DOI: |
10.48350/174029 |
URI: |
https://boris.unibe.ch/id/eprint/174029 |
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