On noncommutative principal bundles with finite abelian structure group

Abstract

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 $\alpha :\Lambda \to \mathrm{Aut}(A)$, 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.