Completions of monoids with applications to the Cuntz semigroup

Details Completions of monoids with applications to the Cuntz semigroup Completions of monoids with applications to the Cuntz semigroup

2010-03-15

arxiv.org/abs/1003.2874v1

Mathematics

Operator Algebras

22 pages, 3 diagrams

Scientific paper

We provide an abstract categorical framework that relates the Cuntz semigroups of the C$^*$-algebras $A$ and $A\otimes \mathcal{K}$. This is done through a certain completion of ordered monoids by adding suprema of countable ascending sequences. Our construction is rather explicit and we show it is functorial and unique up to isomorphism. This approach is used in some applications to compute the stabilized Cuntz semigroup of certain C$^*$-algebras.

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