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
delbarc@unicamp.br
Andrei Moroianu
Lab. de Mathématiques d'Orsay, Université Paris-Saclay, Orsay, France
andrei.moroianu@math.cnrs.fr
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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