Double Principal Bundles

TL;DR

This paper introduces double principal bundles (DPBs), exploring their structure, examples, dualities, gauge transformations, and connections, thereby extending the theory of vector bundles and Lie groups.

Contribution

It defines DPBs, shows their relation to double vector bundles, and investigates dual structures, gauge transformations, and connections within this new framework.

Findings

Double vector bundles can be realized as associated bundles of their frame bundles.

DPBs encompass examples like double Lie groups and double homogeneous spaces.

The paper develops the theory of dual structures, gauge transformations, and connections in DPBs.

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.