The Ternary Structure of Lie Algebroid Connections

Autor:	Bruce, Andrew James
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics 20N10 53D17 58A50 53B05
Zdroj:	Symmetry 2024, 16(6), 725
Druh dokumentu:	Working Paper
DOI:	10.3390/sym16060725
Popis:	We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold. We present some new interpretations of classical results via this ternary structure of connections. Endomorphisms of linear connections are studied, and their ternary structure, in particular the endomorphism truss, is explicitly presented. We remark that the use of ternary structures in differential geometry is novel and that the endomorphism truss of linear connections provides a concrete geometric example of a truss. Comment: A rewritten and extended version that contains further results is published in Symmetry under the title "Heaps of Linear Connections and Their Endomorphism Truss"
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.13327 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.