论文标题
c* - 分子产品的晶格订购的Abelian Semigroups
C*-envelopes of semicrossed products by lattice ordered abelian semigroups
论文作者
论文摘要
半度性产品是一个非偏爱操作员代数，该代数编码了半群在操作员或C*-Algebra上的作用。我们证明，当离散晶格的阳性订单的阳性锥体作用于c*-algebra时，相关的半正值产物的C*Envelope是整个组交叉产品的整个角落。通过构建一个c* - 覆盖本身是交叉产品的完整角落，并计算Shilov理想，我们可以获得对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 $带到了所有离散的晶格订购的Abelian组的类别。
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 discrete 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 Shilov 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 discrete lattice ordered abelian groups.
