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• W3100525232 abstract "We study partial actions of exact discrete groups on C*-algebras. We show that the partial crossed product of a commutative C*-algebra by an exact discrete group is nuclear whenever the full and reduced partial crossed products coincide. This generalises a result by Matsumura in the context of global actions. In general, we prove that a partial action of an exact discrete group on a C*-algebra $A$ has Exel's approximation property if and only if the full and reduced partial crossed products associated to the diagonal partial action on $Aotimes_{max} A^mathrm{op}$ coincide. We apply our results to show that the reduced semigroup C*-algebra $mathrm{C}^*_{lambda}(P)$ of a submonoid of an exact discrete group is nuclear if the left regular representation on $ell^2(P)$ is an isomorphism between the full and reduced C*-algebras. We also show that nuclearity is equivalent to the weak containment property in the case of C*-algebras associated to separated graphs." @default.
• W3100525232 created "2020-11-23" @default.
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• W3100525232 date "2020-11-12" @default.
• W3100525232 modified "2023-09-27" @default.
• W3100525232 title "Nuclearity for partial crossed products by exact discrete groups" @default.
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