Differential groupoids and $C^*$-algebras

TL;DR

This paper introduces a method to construct C*-algebras from differential groupoids, establishing a functorial relationship that connects differential geometric structures with operator algebras.

Contribution

It presents a new construction of C*-algebras from differential groupoids and proves that this construction is functorial, linking differential geometry and operator algebra theory.

Findings

Construction of C*-algebra from differential groupoids

Functorial relationship between differential groupoids and C*-algebras

Establishment of a covariant functor from differential groupoids to C*-algebras

Abstract

The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.