Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras-Reference-Cited by-同舟云学术

Classification of the symmetry Lie algebras for six-dimensional co-dimension two Abelian nilradical Lie algebras

Published:2023 Issue:1 Volume:9 Page:1969-1996
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Almutiben Nouf¹²,Boone Edward L.³,Ghanam Ryad⁴,Thompson G.⁵

Affiliation:

1. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, V. A. 23284, USA

2. Department of Mathematics, College of Sciences, Jouf University, Saudi Arabia; naalswilem@ju.edu.sa

3. Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, V. A. 23284, USA; elboone@vcu.edu

4. Department of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar, Doha, P. O. Box 8095, Doha, Qatar; raghanam@vcu.edu

5. Department of Mathematics, University of Toledo, Toledo, OH 43606, USA; gerard.thompson@utoledo.edu

Abstract

<abstract><p>In this paper, we consider the symmetry algebra of the geodesic equations of the canonical connection on a Lie group. We mainly consider the solvable indecomposable six-dimensional Lie algebras with co-dimension two abelian nilradical that have an abelian complement. In dimension six, there are nineteen such algebras, namely, $ A_{6, 1} $–$ A_{6, 19} $ in Turkowski's list. For each algebra, we give the geodesic equations, a basis for the symmetry Lie algebra in terms of vector fields, and finally we identify the symmetry Lie algebra from standard lists.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference19 articles.

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2. S. Lie, Vorlesungen über differentialgleichungen mit bekannten infinitesimalen transformationen, Leipzig, 1891.

3. P. J. Olver, Applications of Lie groups to differential equations, Springer Science & Business Media, 2000. https://doi.org/10.1007/978-1-4684-0274-2

4. G. W. Bluman, S. Kumei, Symmetries and differential equations, Springer Science & Business Media, 2013. http://doi.org/10.1007/978-1-4757-4307-4

5. D. J. Arrigo, Symmetry analysis of differential equations, John Wiley & Sons, 2015.

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