2024/09/24 by Joan Bosa, Francesc Perera, Bosa, Joan +5
Computer Science · Mathematics · #06B35 #06F05 #46L05 #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2409.16274
openalex publication_date 2024/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.