# Journal of Noncommutative Geometry

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**Volume 8, Issue 4, 2014, pp. 987–1022**

**DOI: 10.4171/JNCG/175**

Published online: 2015-02-02

On noncommutative principal bundles with finite abelian structure group

Stefan Wagner^{[1]}(1) Universität Hamburg, Germany

Let $\Lambda$ be a finite abelian group. A dynamical system with transformation group $\Lambda$ is a triple $(A,\Lambda,\alpha)$, consisting of a unital locally convex algebra $A$, the finite abelian group $\Lambda$ and a group homomorphism $\alpha:\Lambda\rightarrow\Aut(A)$, which induces an action of $\Lambda$ on $A$. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of principal bundles with finite abelian structure group based on such dynamical systems.

*Keywords: *Noncommutative differential geometry, dynamical systems, (trivial) principal bundles with finite abelian structure group, (trivial) noncommutative principal bundles with finite abelian structure group, graded algebras, crossed-product algebras, factor systems

Wagner Stefan: On noncommutative principal bundles with finite abelian structure group. *J. Noncommut. Geom.* 8 (2014), 987-1022. doi: 10.4171/JNCG/175