Journal of Lie Theory

no. 2
Post-Lie Algebra Structure of Manifolds with Constant Curvature and Torsion
Erlend Grong1; Hans Z. Munthe-Kaas1; Jonatan Stava1
1Matematisk Institutt, University of Bergen, Bergen, Norway
Journal of Lie Theory, Volume 34 (2024) no. 2, pp. 339-352
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.
DOI: 10.5802/jolt.1338
Classification: 53C05, 41A58, 53C30,17D99
Keywords: Post-Lie algebras, connections, locally homogeneous spaces spaces

Erlend Grong  1 ; Hans Z. Munthe-Kaas  1 ; Jonatan Stava  1

1 Matematisk Institutt, University of Bergen, Bergen, Norway 
Erlend Grong; Hans Z. Munthe-Kaas; Jonatan 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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     title = {Post-Lie {Algebra} {Structure} of {Manifolds} with {Constant} {Curvature} and {Torsion}},
     journal = {Journal of Lie Theory},
     pages = {339--352},
     year = {2024},
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