Theory of connections on graded principal bundles
May, 199643 pages
Published in:
- Rev.Math.Phys. 10 (1998) 47-80
e-Print:
- dg-ga/9605006 [math.DG]
Report number:
- CPT-96-P-3331
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Abstract:
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.References(17)
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