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arXiv · 2409.16274

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

Joan Bosa·Francesc Perera·Jianchao Wu·Joachim Zacharias
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Abstract

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.

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Joan Bosa, Francesc Perera, Jianchao Wu, Joachim Zacharias. 2024-09-24. The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups. https://arxiv.org/abs/2409.16274

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