论文标题
确切离散组的部分交叉产品的核性
Nuclearity for partial crossed products by exact discrete groups
论文作者
论文摘要
我们研究了确切离散组在C* - 代数上的部分作用。我们表明，每当全部和减少的部分交叉产物重合时，确切的离散组的交换c*代数的部分交叉产物都是核。这将Matsumura的结果概括为在全球行动的背景下。通常，我们证明，当且仅当与$ a \ otimes _ {\ otimes _ {\ max} a^\ mathrm {op conconcience $ a \ otimes _ {\ otimes _ {\ otimes _ {\ otimes _ {\ ot} $ conciencide相关时我们应用结果表明，如果$ \ ell^2（p）$上的左定期表示，则降低的semogroup c*-algebra $ \ algebra $ \ mathrm {c}^*_λ（p）$是核的核代表，如果$ \ ell^2（p）$是完整的和还原的C*-Algebras之间的同构。我们还表明，在与分离图相关的C* - 代数的情况下，核性与弱遏制性质相当。
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 $A\otimes_{\max} A^\mathrm{op}$ coincide. We apply our results to show that the reduced semigroup C*-algebra $\mathrm{C}^*_λ(P)$ 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.
