Cyclic noncommutative covering projections

Abstract

The Gelfand - Naĭmark theorem supplies the one to one correspondence between commutative $C^{\ast }$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^{\ast }$-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.

arXiv comment18 pages, 32 references

References in corpus (5)

• Noncommutative Manifolds the Instanton Algebra and Isospectral Deformations
• Algebras of distributions suitable for phase-space quantum mechanics. I
• Adjoint functors between categories of Hilbert C*-modules
• Equivariant spectral triples on the quantum SU(2) group
• Inverse Limits of Noncommutative Covering Projections