Cuntz Semigroups of Compact-Type Hopf C-Algebras

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 th...

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Bibliographic Details
Published in:Axioms 2017-03, Vol.6 (4), p.1
Main Author: Kučerovský, Dan
Format: Article
Language:English
Subjects:
Algebra
C-algebraic quantum groups
Cuntz semigroup
Group theory
Hopf algebras
Invariants
Isomorphism
multiplicative unitaries
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms6010001