Vector Sheaves Associated with Principal Sheaves

E. Vassiliou

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arXiv · math/9810083

Vector Sheaves Associated with Principal Sheaves

E. Vassiliou

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Abstract

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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BibTeX RIS

E. Vassiliou. 1998-10-13. Vector Sheaves Associated with Principal Sheaves. https://arxiv.org/abs/math/9810083

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