A systematic approach for invariants of C∗-algebras

0582791 - MÚ 2024 RIV PL eng J - Journal Article
Cantier, Laurent
A systematic approach for invariants of C∗-algebras.
Studia mathematica. Roč. 273, č. 1 (2023), s. 63-99. ISSN 0039-3223. E-ISSN 1730-6337
Institutional support: RVO:67985840
Keywords : C∗-algebras * categorical framework * Hausdorffized unitary Cuntz semigroup
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
https://doi.org/10.4064/sm230516-22-6

We define a categorical framework in which we build a systematic construction that provides generic invariants for C∗-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties such as continuity, a metric on the set of morphisms and a theory of ideals and quotients which naturally encapsulates compatibility diagrams. Consequently, any of these invariants appear as good candidates for the classification of non-simple C∗-algebras. Further, most of the existing invariants could be rewritten via this method. As an application, we define a Hausdorffized version of the unitary Cuntz semigroup and explore its potential towards classification results. We indicate several open lines of research.
Permanent Link: https://hdl.handle.net/11104/0350838