C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces

0582707 - MÚ 2025 RIV US eng J - Článek v odborném periodiku
Adamo, M. S. - Archey, D. E. - Forough, Marzieh - Georgescu, M. C. - Jeong, J. A. - Strung, Karen Ruth - Viola, M. G.
C*-algebras associated to homeomorphisms twisted by vector bundles over finite dimensional spaces.
American Mathematical Society. Transactions. Roč. 377, č. 3 (2024), s. 1597-1640. ISSN 0002-9947. E-ISSN 1088-6850
Grant CEP: GA ČR(CZ) GJ19-05271Y; GA ČR(CZ) GJ20-17488Y
Institucionální podpora: RVO:67985840
Klíčová slova: minimal homeomorphisms * C*-correspondences * classification of nuclear C*-algebras
Obor OECD: Pure mathematics
Impakt faktor: 1.3, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1090/tran/8900

In this paper we study Cuntz-Pimsner algebras associated to C*-correspondences over commutative C*-algebras from the point of view of the C*-algebra classification programme. We show that when the correspondence comes from an aperiodic homeomorphism of a finite dimensional infinite compact metric space X twisted by a vector bundle, the resulting Cuntz- Pimsner algebras have finite nuclear dimension. When the homeomorphism is minimal, this entails classification of these C*-algebras by the Elliott invariant. This establishes a dichotomy: when the vector bundle has rank one, the Cuntz-Pimsner algebra has stable rank one. Otherwise, it is purely infinite. For a Cuntz-Pimsner algebra of a minimal homeomorphism of an infinite compact metric space X twisted by a line bundle over X, we introduce orbit breaking subalgebras. With no assumptions on the dimension of X, we show that they are centrally large subalgebras and hence simple and stably finite. When the dimension of X is finite, they are furthermore Z-stable and hence classified by the Elliott invariant.
Trvalý link: https://hdl.handle.net/11104/0350791