Conformal Killing symmetric tensors on Lie groups
Differential Geometry
2023-05-02 v1 Rings and Algebras
Abstract
We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all 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.
Cite
@article{arxiv.2012.08337,
title = {Conformal Killing symmetric tensors on Lie groups},
author = {Viviana del Barco and Andrei Moroianu},
journal= {arXiv preprint arXiv:2012.08337},
year = {2023}
}
Comments
23 pages