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Cuntz Semigroups of Compact-Type Hopf C*-Algebras

Department of Mathematics and Statistics, University of New Brunswick, Fredericton NB E3B 5A3, Canada
Academic Editor: Florin Felix Nichita
Received: 29 November 2016 / Revised: 22 December 2016 / Accepted: 26 December 2016 / Published: 4 January 2017
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2016)
PDF [463 KB, uploaded 4 January 2017]


The classical Cuntz semigroup has an important role in the study of C*-algebras, being one of the main invariants used to classify recalcitrant C*-algebras up to isomorphism. We consider C*-algebras that have Hopf algebra structure, and find additional structure in their Cuntz semigroups. We show that in many cases, isomorphisms of Cuntz semigroups that respect this additional structure can be lifted to Hopf algebra (bi)isomorphisms, up to a possible flip of the co-product. This shows that the Cuntz semigroup provides an interesting invariant of C*-algebraic quantum groups. View Full-Text
Keywords: Cuntz semigroup; Hopf algebras; C*-algebraic quantum groups; multiplicative unitaries Cuntz semigroup; Hopf algebras; C*-algebraic quantum groups; multiplicative unitaries
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Kučerovský, D. Cuntz Semigroups of Compact-Type Hopf C*-Algebras. Axioms 2017, 6, 1.

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