Abstract
We organize colored aromatic trees into a pre-Lie–Rinehart algebra (i.e., a flat torsion-free Lie–Rinehart algebra) endowed with a natural trace map, and show the freeness of this object among pre-Lie–Rinehart algebras with trace. This yields the algebraic foundations of aromatic B-series.
This work was partially supported by the project Pure Mathematics in Norway, funded by Trond Mohn Foundation and Tromsø Research Foundation.
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Acknowledgements
The second author thanks Universitetet i Bergen for the warm welcome and stimulating atmosphere during his two visits in September 2018 and May 2019, and Trond Mohn Foundation for support. He also thanks Camille Laurent-Gengoux for an illuminating e-mail discussion on Lie algebroids.
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Fløystad, G., Manchon, D., Munthe-Kaas, H.Z. (2021). The Universal Pre-Lie–Rinehart Algebras of Aromatic Trees. In: Baklouti, A., Ishi, H. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications . TJC 2019. Springer Proceedings in Mathematics & Statistics, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-030-78346-4_9
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