Separability idempotents in C*-algebras

TL;DR

This paper investigates the concept of separability idempotents within C*-algebras, extending algebraic ideas to operator algebra frameworks, motivated by applications in quantum groupoids.

Contribution

It introduces and analyzes the notion of separability idempotents in C*-algebras, bridging algebraic and operator algebra contexts, especially in relation to quantum groupoids.

Findings

Characterization of separability idempotents in C*-algebras

Extension of algebraic notions to the multiplier algebra framework

Relevance to locally compact quantum groupoids

Abstract

In this paper, we study the notion of a separability idempotent in the C*-algebra framework. This is analogous to the notion in the purely algebraic setting, typically considered in the case of (finite-dimensional) algebras with identity, then later also considered in the multiplier algebra framework by the second-named author. The current work was motivated by the appearance of such objects in the authors' ongoing work on locally compact quantum groupoids.