Invariant Connections in a Non-Abelian Principal Bundle

✍ Scribed by V. Hussin; J. Negro; M.A. Delolmo

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 859 KB
• Volume: 231
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1994.1040

✦ Synopsis

Given a transitive action of a symmetry group (G) on the base space (B) of a non-Abelian principal bundle (\mathscr{P}{t}) with a connection (\omega), we study the way this action can be lifted to a certain action of (G) on (\mathscr{P}{\omega}) leaving invariant (\omega). We show that such an action is described by a two-cocycle of (G) with values on the group of identity lifts, (H_{l}). The general properties of these two-cocycles are investigated and some cases for principal bundles with (S U(n)) as gauge group are worked out. T 1994 Academic Press. Inc.