doi:10.1016/j.laa.2025.07.006engBosa, JoanPerera, FrancescWu, JianchaoZacharias, JoachimThe dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroupsART-2025-144985We 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.2025http://zaguan.unizar.es/record/16240210.1016/j.laa.2025.07.006http://zaguan.unizar.es/record/162402oai:zaguan.unizar.es:162402info:eu-repo/grantAgreement/ES/AEI/CEX2020-001084-Minfo:eu-repo/grantAgreement/ES/MCINN/PID2020-113047GBLINEAR ALGEBRA AND ITS APPLICATIONS 725 (2025), 248-308byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess