The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups

Bosa, Joan (Universidad de Zaragoza) ; Perera, Francesc ; Wu, Jianchao ; Zacharias, Joachim

Resumen: We develop a theory of general quotients for W- and Cu-semigroups beyond the case of quotients by ideals. To this end, we introduce the notion of a normal pair, which allows us to take quotients of W-semigroups in a similar way as normal subgroups arise as kernels of group homomorphisms.
We use this to define the dynamical Cuntz semigroup as the universal object induced from an action of a group G on a W-semigroup. In the C*-algebraic framework, under mild assumptions, the universality of this dynamical invariant helps us tap into the structure of the Cuntz semigroup of crossed product C*-algebras.

Idioma: Inglés

DOI: 10.1016/j.laa.2025.07.006

Año: 2025

Publicado en: LINEAR ALGEBRA AND ITS APPLICATIONS 725 (2025), 248-308
ISSN: 0024-3795

Financiación: info:eu-repo/grantAgreement/ES/AEI/CEX2020-001084-M
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2020-113047GB

Tipo y forma: Article (Published version)

Área (Departamento): Área Algebra (Dpto. Matemáticas)