
Journal of Lie Theory 34 (2024), No. 2, 339352 Copyright Heldermann Verlag 2024 PostLie Algebra Structure of Manifolds with Constant Curvature and Torsion Erlend Grong Matematisk Institutt, University of Bergen, Bergen, Norway erlend.grong@uib.no Hans Z. MuntheKaas Matematisk Institutt, University of Bergen, Bergen, Norway hans.munthekaas@uib.no Jonatan Stava Matematisk Institutt, University of Bergen, Bergen, Norway jonatan.stava@uib.no For a general affine connection with parallel torsion and curvature, we show that a postLie algebra structure exists on its space of vector fields, generalizing previous results for flat connections. However, for nonflat 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 postLie algebra and give applications for solving differential equations on manifolds. Keywords: PostLie algebras, connections, locally homogeneous spaces spaces. MSC: 53C05, 41A58, 53C30,17D99. [ Fulltextpdf (153 KB)] for subscribers only. 