000162402 001__ 162402 000162402 005__ 20251017144601.0 000162402 0247_ $$2doi$$a10.1016/j.laa.2025.07.006 000162402 0248_ $$2sideral$$a144985 000162402 037__ $$aART-2025-144985 000162402 041__ $$aeng 000162402 100__ $$0(orcid)0000-0001-9442-1583$$aBosa, Joan$$uUniversidad de Zaragoza 000162402 245__ $$aThe dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups 000162402 260__ $$c2025 000162402 5060_ $$aAccess copy available to the general public$$fUnrestricted 000162402 5203_ $$aWe 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. 000162402 536__ $$9info:eu-repo/grantAgreement/ES/AEI/CEX2020-001084-M$$9info:eu-repo/grantAgreement/ES/MCINN/PID2020-113047GB 000162402 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000162402 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000162402 700__ $$aPerera, Francesc 000162402 700__ $$aWu, Jianchao 000162402 700__ $$aZacharias, Joachim 000162402 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra 000162402 773__ $$g725 (2025), 248-308$$pLinear algebra appl.$$tLINEAR ALGEBRA AND ITS APPLICATIONS$$x0024-3795 000162402 8564_ $$s2629601$$uhttps://zaguan.unizar.es/record/162402/files/texto_completo.pdf$$yVersión publicada 000162402 8564_ $$s1598103$$uhttps://zaguan.unizar.es/record/162402/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000162402 909CO $$ooai:zaguan.unizar.es:162402$$particulos$$pdriver 000162402 951__ $$a2025-10-17-14:14:12 000162402 980__ $$aARTICLE