The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups
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| Názov: | The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups |
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| Autori: | Joan Bosa, Francesc Perera, Jianchao Wu, Joachim Zacharias |
| Zdroj: | Zaguán. Repositorio Digital de la Universidad de Zaragoza Universidad de Zaragoza |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Elsevier BV, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Mathematics - Operator Algebras, FOS: Mathematics, 06B35, 06F05, 46L05, Mathematics - Category Theory, Category Theory (math.CT), Operator Algebras (math.OA) |
| Popis: | 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. 49 pages |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2025.07.006 |
| DOI: | 10.48550/arxiv.2409.16274 |
| Prístupová URL adresa: | http://arxiv.org/abs/2409.16274 http://zaguan.unizar.es/record/162402 |
| Rights: | CC BY arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....c0884ef5a298d92b5d9c24ab9fb8c1cc |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | 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.<br />49 pages |
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| ISSN: | 00243795 |
| DOI: | 10.1016/j.laa.2025.07.006 |