2017/01/04 by Dan Kučerovský, Dan Kucerovsky
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Algebra over a field #Holomorphic and Operator Theory #Hopf algebra #Invariant (physics) #Quantum #Semigroup #math.KT #math.OA #msc:16T05 #msc:16T2 #msc:47L50 #msc:47L80
paper · pdf · doi:10.3390/axioms6010001
published as D. Kucerovsky, Cuntz semigroups of compact-type Hopf C*-algebras, Axioms (2017), 6(1),1, 21 pages · Keywords: Cuntz semigroup, Hopf algebras, equivariant Cuntz semigroup, C*-algebraic quantum groups, multiplicative unitaries
openalex publication_date 2017/01/04 · openalex created_date 2017/01/13 · arxiv created 2018/02/20 · arxiv updated 2018/02/21 · openalex updated_date 2026/08/05
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.