46A55 — 1 articles found.

The Cuntz Semigroup of the Tensor Product of C*-algebras

C. R. Math. Rep. Acad. Sci. Canada Vol. 41 (2) 2019, pp. 32-44
Vol.41 (2) 2019
George A. Elliott; Cristian Ivanescu; Dan Kucerovsky Details
(Received: 2014-12-08 , Revised: 2019-10-24 )
(Received: 2014-12-08 , Revised: 2019-10-24 )

George A. Elliott,Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4; e-mail: elliott@math.toronto.edu

Cristian Ivanescu.Department of Mathematics and Statistics, MacEwan University, Edmonton, Alberta, Canada T5J 4S2; e-mail: IvanescuC@macewan.ca

Dan Kurcerovsky.Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, Canada E38 5A3; e-mail: dkucerov@unb.ca

Abstract/Résumé:

We calculate the Cuntz semigroup of the tensor product of two C\(^*\)-algebras, restricting attention to the case that the Cuntz semigroup, both for the given algebras and for the tensor product, is given by affine functions. We show that the answer is the universal Cuntz category tensor product of Antoine et al. (2018).

On démontre que, dans certains cas, le semigroupe de Cuntz du produit tensoriel de deux C\(^*\)-algèbres est le produit tensoriel dans la catégorie de Cuntz.

Keywords: C*-algebra tensor product, Cuntz Semigroup, tracial cone

AMS Subject Classification: Convex sets in topological linear spaces; Choquet theory, General theory of $C^*$-algebras 46A55, 46L05

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