Volume 28, Issue 2, June 2021, Pages 242 - 253
Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case
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: firstname.lastname@example.org
Received 11 November 2020, Accepted 13 March 2021, Available Online 10 April 2021.
- 10.2991/jnmp.k.210401.001How to use a DOI?
- Lie group; canonical connection; geodesic system; Lie symmetry
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.
- © 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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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 -