论文标题
典型类别，限制性半群及其操作员代数
Étale categories, restriction semigroups, and their operator algebras
论文作者
论文摘要
我们定义了与典型的类别和限制性半群相关的全部和减少的非自我支持操作员代数，回答了Kudryavtseva和Lawson在\ cite {Lawson}中提出的问题。此外，我们定义了限制性半群在$ C^*$ - 代数上的典型分数的分号代数，当将限制性半igroup的操作员代数与其相关e tale类别的操作员代数连接到操作员代数时，这是关键点。我们还证明，在特定情况下，典型的groupoid和反向半群，我们的操作员代数与引用对象的$ c^*$ - 代数相吻合。
We define the full and reduced non-self-adjoint operator algebras associated with étale categories and restriction semigroups, answering a question posed by Kudryavtseva and Lawson in \cite{lawson}. Moreover, we define the semicrossed product algebra of an étale action of a restriction semigroup on a $C^*$-algebra, which turns out to be the key point when connecting the operator algebra of a restriction semigroup with the operator algebra of its associated étale category. We also prove that in the particular cases of étale groupoids and inverse semigroups our operator algebras coincide with the $C^*$-algebras of the referred objects.
