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

0571082 - MÚ 2024 RIV US eng J - Článek v odborném periodiku
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
Institucionální podpora: RVO:67985840
Klíčová slova: Cu-metric * K1-obstructions * one-dimensional NCCW * unitary Cuntz semigroup
Obor OECD: Pure mathematics
Impakt faktor: 1.3, rok: 2022
Způsob publikování: Omezený přístup
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.
Trvalý link: https://hdl.handle.net/11104/0342387