Journal of Noncommutative Geometry

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Volume 12, Issue 3, 2018, pp. 997–1040
DOI: 10.4171/JNCG/296

Published online: 2018-10-30

Separability idempotents in $C^*$-algebras

Byung-Jay Kahng[1] and Alfons Van Daele[2]

(1) Canisius College, Buffalo, USA
(2) University of Leuven, Belgium

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.

Keywords: Separability idempotent, weak multiplier Hopf algebra, locally compact quantum groupoid

Kahng Byung-Jay, Van Daele Alfons: Separability idempotents in $C^*$-algebras. J. Noncommut. Geom. 12 (2018), 997-1040. doi: 10.4171/JNCG/296