Journal of Nonlinear Mathematical Physics

In Press, Corrected Proof, Available Online: 10 April 2021

Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case

Authors
Hassan Almusawa1, *, Ryad Ghanam2, Gerard Thompson3
1Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia
2Department of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar, PO Box 8095, Doha, Qatar
3Department of Mathematics, University of Toledo, Toledo, OH 43606, U.S.A.
*Corresponding author: Email: haalmusawa@jazanu.edu.sa
Corresponding Author
Hassan Almusawa
Received 11 November 2020, Accepted 13 March 2021, Available Online 10 April 2021.
DOI
https://doi.org/10.2991/jnmp.k.210401.001How to use a DOI?
Keywords
Lie group, canonical connection, geodesic system, Lie symmetry
Abstract

This paper studies the canonical symmetric connection ∇ associated to any Lie group G. The salient properties of ∇ are stated and proved. The Lie symmetries of the geodesic system of a general linear connection are formulated. The results are then applied to ∇ in the special case where the Lie algebra 𝔤 of G, has a codimension one abelian nilradical. The conditions that determine a Lie symmetry in such a case are completely integrated. Finally the results obtained are compared with some four-dimensional Lie groups whose Lie algebras have three-dimensional abelian nilradicals, for which the calculations were performed by MAPLE.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Publication Date
2021/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.k.210401.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Hassan Almusawa
AU  - Ryad Ghanam
AU  - Gerard Thompson
PY  - 2021
DA  - 2021/04
TI  - Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case
JO  - Journal of Nonlinear Mathematical Physics
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.210401.001
DO  - https://doi.org/10.2991/jnmp.k.210401.001
ID  - Almusawa2021
ER  -