Completions of monoids with applications to the Cuntz semigroup

2010/03/15 by Ramon Antoine, Antoine, Ramon, Joan Bosa +3
Mathematics · #06F05 #19K14 #46L35 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #math.OA #math.RA #msc:06F05 #msc:19K14 #msc:46L35

paper · pdf · doi:10.48550/arxiv.1003.2874

22 pages, 3 diagrams

arxiv created 2010/03/15 · arxiv updated 2010/03/16

Abstract

We provide an abstract categorical framework that relates the Cuntz semigroups of the C^*-algebras A and A⊗ 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.

Related

• The modern theory of Cuntz semigroups of C*-algebras
• Pullbacks, C(X)-algebras, and their Cuntz semigroup
• The Cuntz semigroup as an invariant for C*-algebras
• A total Cuntz semigroup for C^*-algebras of stable rank one
• C^*-algebras generated by the paths semigroup