Double Principal Bundles

Abstract

We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and connections in DPBs are investigated.

20 pages. This is a replacement of arXiv:1611.00672 with the same title. We add Proposition 2.11 and clarify some notations

References in corpus (5)

• $Q$-Manifolds and Mackenzie Theory
• Graded Geometry, $Q$-Manifolds, and Microformal Geometry
• N-manifolds of degree 2 and metric double vector bundles
• The Geometrisation of $\mathbb{N}$-manifolds of degree 2
• Duality and triple structures

Cited by in corpus (1)

• Categorification of VB-Lie algebroids and VB-Courant algebroids