Journal of Nonlinear Mathematical Physics

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Volume 28, Issue 2, June 2021, Pages 242 - 253

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
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 βˆ‡ associated to any Lie group G. The salient properties of βˆ‡ are stated and proved. The Lie symmetries of the geodesic system of a general linear connection are formulated. The results are then applied to βˆ‡ in the special case where the Lie algebra 𝔀 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
Β© 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
Volume-Issue
28 - 2
Pages
242 - 253
Publication Date
2021/04/10
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.k.210401.001How to use a DOI?
Copyright
Β© 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

risenwbib
TY  - JOUR
AU  - Hassan Almusawa
AU  - Ryad Ghanam
AU  - Gerard Thompson
PY  - 2021
DA  - 2021/04/10
TI  - Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case
JO  - Journal of Nonlinear Mathematical Physics
SP  - 242
EP  - 253
VL  - 28
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.210401.001
DO  - 10.2991/jnmp.k.210401.001
ID  - Almusawa2021
ER  -