Quantization of Noncompact Coverings and Strong Morita Equivalence

TL;DR

This paper establishes that in the noncommutative setting, finite-fold coverings are equivalent to strong Morita equivalences, extending classical algebraic Galois covering results to $C^*$-algebras.

Contribution

It proves that noncommutative finite-fold coverings correspond to strong Morita equivalences, generalizing algebraic Galois covering concepts to $C^*$-algebras.

Findings

Noncommutative finite-fold coverings are equivalent to strong Morita equivalences.

Extension of classical Galois covering results to $C^*$-algebra framework.

Abstract

Any finite algebraic Galois covering corresponds to an algebraic Morita equivalence. Here the $C^*$-algebraic analog of this fact is proven, i.e. any noncommutative finite-fold covering corresponds to a strong Morita equivalence.