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Journal of Lie Theory 32 (2022), No. 1, 001--022
Copyright Heldermann Verlag 2022

Conformal Killing Symmetric Tensors on Lie Groups

Viviana Del Barco
Inst. de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Brasil

Andrei Moroianu
Lab. de Mathématiques d'Orsay, Université Paris-Saclay, Orsay, France

We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all left-invariant conformal Killing symmetric tensors are sums of Killing tensors and multiples of the metric tensor. We show that if a Lie algebra is either 2-step nilpotent, or 2- or 3-dimensional, or 4-dimensional non-solvable, or 4-dimensional solvable with 1-dimensional derived ideal, or has an abelian factor, then it is of Killing type with respect to any positive definite metric.

Keywords: Conformal Killing tensors, Riemannian Lie groups.

MSC: 53D25, 22E25, 53C30, 22E15.

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