Cyclic noncommutative covering projections

TL;DR

This paper develops an algebraic framework for noncommutative covering projections with finite cyclic groups, extending topological concepts to noncommutative $C^*$-algebras.

Contribution

It introduces a purely algebraic construction of noncommutative covering projections with finite cyclic groups of transformations.

Findings

Provides a new algebraic method for noncommutative coverings

Extends topological invariants to noncommutative settings

Bridges the gap between algebraic and topological approaches

Abstract

The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological space. Generalizations of several topological invariants can be defined by algebraical methods. This article contains a pure algebraical construction of (noncommutative) covering projections with finite cyclic groups of covering transformations.