The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Bosa, Joan Perera, Francesc Wu, Jianchao Zacharias, Joachim |
| author_facet | Bosa, Joan Perera, Francesc Wu, Jianchao Zacharias, Joachim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16274 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups Bosa, Joan Perera, Francesc Wu, Jianchao Zacharias, Joachim Operator Algebras Category Theory 06B35, 06F05, 46L05 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. |
| title | The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups |
| topic | Operator Algebras Category Theory 06B35, 06F05, 46L05 |
| url | https://arxiv.org/abs/2409.16274 |