Theory of connections on graded principal bundles

Details Theory of connections on graded principal bundles Theory of connections on graded principal bundles

1996-05-16

arxiv.org/abs/dg-ga/9605006v1

Rev.Math.Phys. 10 (1998) 47-80

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, no figures, 94Kb tar gzipped file which includes special macros and fonts (prep.tex is the source TeX file), also av

Scientific paper

The geometry of graded principal bundles is discussed in the framework of graded manifold theory of Kostant-Berezin-Leites. In particular, we prove that a graded principal bundle is globally trivial if and only if it admits a global graded section and, further, that the sheaf of vertical derivations on such a bundle coincides with the graded distribution induced by the action of the structure graded Lie group. This result leads to a natural definition of the graded connection in terms of graded distributions; its relation with Lie superalgebra-valued graded differential forms is also exhibited. Finally, we define the curvature for the graded connection; we prove that the curvature controls the involutivity of the horizontal graded distribution corresponding to the graded connection.

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