English

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

Operator Algebras 2022-10-25 v3

Abstract

This paper argues that the unitary Cuntz semigroup, introduced in [10] and termed Cu1_1, 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_1-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_1 alone.

Keywords

Cite

@article{arxiv.2111.06926,
  title  = {The unitary Cuntz semigroup on the classification of non-simple C*-algebras},
  author = {Laurent Cantier},
  journal= {arXiv preprint arXiv:2111.06926},
  year   = {2022}
}

Comments

23 pages - Small changes made for acceptation in Journal of Journal of Mathematical Analysis and Applications