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Journal of Lie Theory 30 (2020), No. 1, 155--169
Copyright Heldermann Verlag 2020

On the Symmetries of Five-Dimensional Solvable Lie Groups

Assia Mostefaoui
Ecole Nationale Polytechnique d'Oran, El M'naouar, Oran 31000, Algeria

Lakehal Belarbi
Dept. of Mathematics, Lab. of Pure and Applied Mathematics, University of Mostaganem, 27000 Mostaganem, Algeria

We consider the five-dimensional solvable Lie group, equipped with left-invariant Riemannian metric. We obtain a full classification of Killing and affine vector fields as well as Ricci, curvature and matter collineations.

Keywords: Solvable Lie group, Killing vector fields, affine vector fields, Ricci collineations, curvature collineations.

MSC: 53C50, 53B30.

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