The Unique Path Lifting for Noncommutative Covering Projections

TL;DR

This paper generalizes the classical topological path lifting problem to noncommutative geometry, demonstrating that paths of *-automorphisms satisfy a unique path lifting property despite the absence of points and paths.

Contribution

It introduces a noncommutative version of the path lifting theorem, focusing on paths of *-automorphisms in noncommutative geometry.

Findings

Paths of *-automorphisms obey unique path lifting

Noncommutative geometry lacks points but retains path concepts

The result extends classical topological ideas to noncommutative settings

Abstract

This article contains a noncommutative generalization of the topological path lifting problem. Noncommutative geometry has no paths and even points. However there are paths of *-automorphisms. It is proven that paths of *-automorphisms comply with unique path lifting.