On Noncommutative Principal Bundles with Finite Abelian Structure Group

TL;DR

This paper introduces a geometrically oriented framework for studying noncommutative principal bundles with finite abelian groups using dynamical systems on unital locally convex algebras.

Contribution

It develops a new approach to noncommutative geometry of principal bundles with finite abelian groups based on dynamical systems.

Findings

Provides a new geometric perspective on noncommutative principal bundles.

Establishes a framework connecting dynamical systems with noncommutative geometry.

Lays groundwork for further exploration of noncommutative fiber bundles.

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 $\alpha:\Lambda\rightarrow\Aut(A)$, 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.