Corpus ID: 229222112

Unitary Cuntz semigroups of ideals and quotients.

@article{Cantier2020UnitaryCS,
  title={Unitary Cuntz semigroups of ideals and quotients.},
  author={Laurent Cantier},
  journal={arXiv: Operator Algebras},
  year={2020}
}
  • Laurent Cantier
  • Published 15 December 2020
  • Mathematics
  • arXiv: Operator Algebras
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 complete lattice structure. In fact, we prove that for any separable C*-algebra with stable rank one A, the assignment $\,$ I $\mapsto$ Cu$_1$(I) defines a complete lattice isomorphism between Lat(A) and Lat(Cu$_1$(A)). Further, we introduce the notion of quotient ideals and exactness for the (non… Expand
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