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

0571082 - MÚ 2024 RIV US eng J - Journal Article
Cantier, Laurent
The unitary Cuntz semigroup on the classification of non-simple C*-algebras.
Journal of Mathematical Analysis and Applications. Roč. 522, č. 2 (2023), č. článku 127003. ISSN 0022-247X. E-ISSN 1096-0813
Institutional support: RVO:67985840
Keywords : Cu-metric * K1-obstructions * one-dimensional NCCW * unitary Cuntz semigroup
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jmaa.2023.127003

This paper argues that the unitary Cuntz semigroup, introduced in [10] 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 K1-groups and their Cuntz semigroups (termed Cu) 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.
Permanent Link: https://hdl.handle.net/11104/0342387