Mathematics – Differential Geometry
Scientific paper
1998-10-13
Mathematics
Differential Geometry
LaTeX, 11 pages, to be published in the Proceedings of the 2nd Conference of Balkan Soc. of Geometers, Thessaloniki, 1998
Scientific paper
In the framework of Abstract Differential Geometry, we show that to a given principal sheaf and a representation of its stuctural sheaf in $A^n$, where A is a sheaf of associative, commutative, unital algebras (over R or C), we associate a vector sheaf. Moreover, under some natural assumptions on the compatibility of the representation with the Maurer-Cartan (or, logarithmic) differentials of the structural sheaves involved, we also show that the connections of the principal sheaf induce A-connections of the associated vector sheaf. We thus recover a result of the classical Differential Geometry within a purely algebro-topological context, without any smoothness assumption.
No associations
LandOfFree
Vector Sheaves Associated with Principal Sheaves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Vector Sheaves Associated with Principal Sheaves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vector Sheaves Associated with Principal Sheaves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-619558