论文标题
Zappa-Szép群体在产品系统上的行动
Zappa-Szép actions of groups on product systems
论文作者
论文摘要
让$ g $是一个组，$ x $是半群$ p $的产品系统。假设$ g $在$ p $上有左动作，$ p $在$ g $上具有正确的操作，因此可以形成Zappa-Szép产品$ P \ Bowtie G $。我们在$ x $上定义了$ g $ $ g $的Zappa-SzépAction，这是$ x $上的一系列功能，这些功能与$ p \ bowtie g $在某种意义上都兼容。如果在$ x $上进行$ g $的Zappa-szép动作，我们在$ p \ bowtie g $上构建了一个新产品$ x \ bowtie g $，称为$ x $ by $ g $的Zappa-Szép产品。然后，我们将$ x \ bowtie g $ $几个通用的C*-代代代代代数与他们各自的hao-ng同构同构相关联。一个特殊的案例是Zappa-Szép动作是同质的。这种情况自然会概括有关文献中产品系统的小组行动。在这种情况下，除了Zappa-Szép产品系统$ X \ Bowtie G $外，还可以构建一种新型的Zappa-Szép产品$ x \ widetilde \ widetilde \ bowtie g $ if $ p $。这两种类型的Zappa-Szép产品系统及其相关的C* - 代数之间出现了一些基本差异。
Let $G$ be a group and $X$ be a product system over a semigroup $P$. Suppose $G$ has a left action on $P$ and $P$ has a right action on $G$, so that one can form a Zappa-Szép product $P\bowtie G$. We define a Zappa-Szép action of $G$ on $X$ to be a collection of functions on $X$ that are compatible with both actions from $P\bowtie G$ in a certain sense. Given a Zappa-Szép action of $G$ on $X$, we construct a new product system $X\bowtie G$ over $P\bowtie G$, called the Zappa-Szép product of $X$ by $G$. We then associate to $X\bowtie G$ several universal C*-algebras and prove their respective Hao-Ng type isomorphisms. A special case of interest is when a Zappa-Szép action is homogeneous. This case naturally generalizes group actions on product systems in the literature. For this case, besides the Zappa-Szép product system $X\bowtie G$, one can also construct a new type of Zappa-Szép product $X \widetilde\bowtie G$ over $P$. Some essential differences arise between these two types of Zappa-Szép product systems and their associated C*-algebras.
