Vector Sheaves Associated with Principal Sheaves

Details Vector Sheaves Associated with Principal Sheaves Vector Sheaves Associated with Principal Sheaves

1998-10-13

arxiv.org/abs/math/9810083v1

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.

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