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

Autor:	Grong, Erlend, Munthe-Kaas, Hans Z., Stava, Jonatan
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry 53C05 (primary) 41A58 53C30 17D99
Zdroj:	Journal of Lie Theory 34 (2024), No. 2, 339--352
Druh dokumentu:	Working Paper
Popis:	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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.02688 Zobrazit plný text záznamu View this record from Arxiv