KK-THEORY OF CIRCLE ACTIONS WITH THE ROKHLIN PROPERTY
Artikel i vetenskaplig tidskrift, 2025

We investigate the structure of circle actions with the Rokhlin property, particularly in relation to equivariant KK-theory. Our main results are T-equivariant versions of celebrated results of Kirchberg: any Rokhlin action on a separable, nuclear C*-algebra is KKT-equivalent to a Rokhlin action on a Kirchberg algebra; and two circle actions with the Rokhlin property on a Kirchberg algebra are conjugate if and only if they are KKT-equivalent. In the presence of the UCT, KKT-equivalence for Rokhlin actions reduces to isomorphism of a K-theoretical invariant, namely of a canonical pure extension naturally associated to any Rokhlin action, and we provide a complete description of the extensions that arise from actions on nuclear C∗-algebras. In contrast with the non-equivariant setting, we exhibit an example showing that an isomorphism between the KT-theories of Rokhlin actions on Kirchberg algebras does not necessarily lift to a KKT-equivalence; this is the first example of its kind, even in the absence of the Rokhlin property.

Författare

Eusebio Gardella

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Canadian Journal of Mathematics

0008-414X (ISSN) 1496-4279 (eISSN)

Vol. In Press

Ämneskategorier (SSIF 2025)

Data- och informationsvetenskap (Datateknik)

DOI

10.4153/S0008414X25000112

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Senast uppdaterat

2025-03-14