Inverse Limits of 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 inverse limits in the category of (noncommutative) covering projections. It is proven that Moyal planes are inverse limits of covering projections of noncommutative tori.

50 pages, 24 references

References in corpus (3)

• Algebras of distributions suitable for phase-space quantum mechanics. I
• Adjoint functors between categories of Hilbert C*-modules
• Infinite Noncommutative Covering Projections

Cited by in corpus (1)

• Cyclic noncommutative covering projections