A semicrossed product is a non-selfadjoint operator algebra encoding the action of a semigroup on an operator or C*-algebra. We prove that, when the positive cone of a lattice ordered abelian group acts on a C*-algebra, the C*-envelope of the associated semicrossed product is a full corner of a crossed product by the whole group. By constructing a C*-cover that itself is a full corner of a crossed product, and computing the Silov ideal, we obtain an explicit description of the C*-envelope. This generalizes a result of Davidson, Fuller, and Kakariadis from $\mathbb{Z}_+^n$ to the class of all lattice ordered abelian groups.

中文翻译：

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格序阿贝尔半群的半交叉积的 C*-包络

半交叉积是一种非自伴随算子代数，编码半群对算子或 C*-代数的作用。我们证明，当晶格有序阿贝尔群的正锥作用于C*-代数时，相关半交叉积的C*-包络是整个群的交叉积的完整角。通过构造一个 C*-cover，它本身就是一个交叉积的完整角，并计算 Silov 理想，我们获得了 C*-envelope 的明确描述。这将戴维森、富勒和卡卡里亚迪斯的结果从 $\mathbb{Z}_+^n$ 推广到所有格有序阿贝尔群的类。