Lie Symmetries of the Canonical Connection: Codimension One Abelian Nilradical Case
- https://doi.org/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/).
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 -