Journal of Lie Theory

no. 1
Conformal Killing Symmetric Tensors on Lie Groups
Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 1-22
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.
DOI: 10.5802/jolt.1217
Classification: 53D25, 22E25, 53C30, 22E15
Keywords: Conformal Killing tensors, Riemannian Lie groups 
@article{JOLT_2022_32_1_a0,
     author = {V. Del Barco and A. Moroianu},
     title = {Conformal {Killing} {Symmetric} {Tensors} on {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {1--22},
     year = {2022},
     volume = {32},
     number = {1},
     doi = {10.5802/jolt.1217},
     zbl = {1494.53066},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1217/}
}
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V. Del Barco; A. Moroianu. Conformal Killing Symmetric Tensors on Lie Groups. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 1-22. doi: 10.5802/jolt.1217

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