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 $α:Λ\rightarrow\Aut(A)$, 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.

35 pages, all comments are welcome. This paper is an improved version of the preprint arXiv:1201.1748v2 [math.DG]

References in corpus (5)

• Noncommutative Geometry Approach to Principal and Associated Bundles
• Principal noncommutative torus bundles
• A Geometric Approach to Noncommutative Principal Torus Bundles
• Free Group Actions from the Viewpoint of Dynamical Systems
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Cited by in corpus (4)

• Part I, Free Actions of Compact Abelian Groups on C*-Algebras
• Noncommutative Coverings of Quantum Tori
• A Note on Twisted Crossed Products and Spectral Triples
• Noncommutative Geometry of Quantized Coverings