• Corpus ID: 244117356

The unitary Cuntz semigroup on the classification of non-simple C*-algebras

@inproceedings{Cantier2021TheUC,
  title={The unitary Cuntz semigroup on the classification of non-simple C*-algebras},
  author={Laurent Cantier},
  year={2021}
}
This paper argues that the unitary Cuntz semigroup, introduced in [9] and termed Cu1, contains crucial information regarding the classification of non-simple C-algebras. We exhibit two (non-simple) C-algebras that agree on their Cuntz semigroups, termed Cu, and their K1-groups and yet disagree at level of their unitary Cuntz semigroups. In the process, we establish that the unitary Cuntz semigroup contains rigorously more information about non-simple C-algebras than Cu and K1 alone. 
Unitary Cuntz semigroups of ideals and quotients.
We define a notion of ideals in the category of ordered monoids satisfying the Cuntz axioms introduced in [2] and termed Cu$^\sim$. We show that the set of ideals of a Cu$^\sim$-semigroup $S$ has a

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