Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion

E. Grong; H. Z. Munthe-Kaas; J. Stava

doi:10.5802/jolt.1338

E. Grong; H. Z. Munthe-Kaas; J. Stava

Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 339-352

Abstract

For a general affine connection with parallel torsion and curvature, we show that a post-Lie algebra structure exists on its space of vector fields, generalizing previous results for flat connections. However, for non-flat connections, the vector fields alone are not enough, as the presence of curvature also necessitates that we include endomorphisms corresponding to infinitesimal actions of the holonomy group. We give details on the universal Lie algebra of this post-Lie algebra and give applications for solving differential equations on manifolds.

arXiv Zbl

DOI: 10.5802/jolt.1338

Classification: 53C05, 41A58, 53C30,17D99
Keywords: Post-Lie algebras, connections, locally homogeneous spaces spaces

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     author = {E. Grong and H. Z. Munthe-Kaas and J. Stava},
     title = {Post-Lie {Algebra} {Structure} of {Manifolds} with {Constant} {Curvature} and {Torsion}},
     journal = {Journal of Lie Theory},
     pages = {339--352},
     year = {2024},
     volume = {34},
     number = {2},
     doi = {10.5802/jolt.1338},
     zbl = {1543.53021},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1338/}
}

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E. Grong; H. Z. Munthe-Kaas; J. Stava. Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion. Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 339-352. doi: 10.5802/jolt.1338

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