An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups

Véronique Fischer; Francesca Tripaldi

doi:10.1016/j.aim.2023.109192

An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups

Véronique Fischer, Francesca Tripaldi

Department of Mathematical Sciences

Scuola Normale Superiore di Pisa

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

Abstract

In this paper, we consider the Rumin complex on homogenenous nilpotent Lie groups. We present an alternative construction to the classical one on Carnot groups using ideas from parabolic geometry. We also give the explicit computations for the Engel group with this approach.

Original language	English
Article number	109192
Journal	Advances in Mathematics
Volume	429
Early online date	11 Jul 2023
DOIs	https://doi.org/10.1016/j.aim.2023.109192
Publication status	Published - 15 Sept 2023

Bibliographical note

Funding Information:
F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978 , Analytic and geometric structures in singular spaces.

Funding Information:
Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037, Quantum limits for sub-elliptic operators.F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978, Analytic and geometric structures in singular spaces.

Funding Information:
Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037 , Quantum limits for sub-elliptic operators.

Funding

F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978 , Analytic and geometric structures in singular spaces. Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037, Quantum limits for sub-elliptic operators.F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978, Analytic and geometric structures in singular spaces. Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037 , Quantum limits for sub-elliptic operators.

Keywords

Cohomology on Lie groups
Engel group
Homogeneous nilpotent Lie groups
Rumin complex on Carnot groups

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1016/j.aim.2023.109192Licence: CC BY

https://arxiv.org/abs/2208.11118Licence: CC BY-NC-SA

Cite this

@article{5aedf26ebdda4a8fb9490af049bce5d6,

title = "An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups",

abstract = "In this paper, we consider the Rumin complex on homogenenous nilpotent Lie groups. We present an alternative construction to the classical one on Carnot groups using ideas from parabolic geometry. We also give the explicit computations for the Engel group with this approach.",

keywords = "Cohomology on Lie groups, Engel group, Homogeneous nilpotent Lie groups, Rumin complex on Carnot groups",

author = "V{\'e}ronique Fischer and Francesca Tripaldi",

note = "Funding Information: F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978 , Analytic and geometric structures in singular spaces. Funding Information: Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037, Quantum limits for sub-elliptic operators.F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978, Analytic and geometric structures in singular spaces. Funding Information: Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037 , Quantum limits for sub-elliptic operators. ",

year = "2023",

month = sep,

day = "15",

doi = "10.1016/j.aim.2023.109192",

language = "English",

volume = "429",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Elsevier Academic Press Inc",

}

TY - JOUR

T1 - An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups

AU - Fischer, Véronique

AU - Tripaldi, Francesca

N1 - Funding Information: F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978 , Analytic and geometric structures in singular spaces. Funding Information: Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037, Quantum limits for sub-elliptic operators.F. Tripaldi is supported by the Swiss National Science Foundation Grant nr. 200020-191978, Analytic and geometric structures in singular spaces. Funding Information: Acknowledgements. V. Fischer acknowledges the support of The Leverhulme Trust via Research Project Grant 2020-037 , Quantum limits for sub-elliptic operators.

PY - 2023/9/15

Y1 - 2023/9/15

N2 - In this paper, we consider the Rumin complex on homogenenous nilpotent Lie groups. We present an alternative construction to the classical one on Carnot groups using ideas from parabolic geometry. We also give the explicit computations for the Engel group with this approach.

AB - In this paper, we consider the Rumin complex on homogenenous nilpotent Lie groups. We present an alternative construction to the classical one on Carnot groups using ideas from parabolic geometry. We also give the explicit computations for the Engel group with this approach.

KW - Cohomology on Lie groups

KW - Engel group

KW - Homogeneous nilpotent Lie groups

KW - Rumin complex on Carnot groups

UR - http://www.scopus.com/inward/record.url?scp=85164408583&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2023.109192

DO - 10.1016/j.aim.2023.109192

M3 - Article

AN - SCOPUS:85164408583

SN - 0001-8708

VL - 429

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 109192

ER -

An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this