论文标题
逆半摩托动作和表示形式
Inverse Semigroupoid Actions and Representations
论文作者
论文摘要
我们表明，在$ x $上的groupoid $ g $的部分操作与Exel的反向半摩群的逆向半摩群$ s（g）$在$ x $上的逆半摩圈动作之间存在一对一的对应关系。 We also define inverse semigroupoid representations on a Hilbert space $H$, as well as the Exel's partial groupoid $C^*$-algebra $C_p^*(G)$, and we prove that there is a one-to-one correspondence between partial groupoid representations of $G$ on $H$, inverse semigroupoid representations of $S(G)$ on $H$ and $C^*$-algebra representations of $ c_p^*（g）$ h $。
We show that there is a one-to-one correspondence between the partial actions of a groupoid $G$ on a set $X$ and the inverse semigroupoid actions of the Exel's inverse semigroupoid $S(G)$ on $X$. We also define inverse semigroupoid representations on a Hilbert space $H$, as well as the Exel's partial groupoid $C^*$-algebra $C_p^*(G)$, and we prove that there is a one-to-one correspondence between partial groupoid representations of $G$ on $H$, inverse semigroupoid representations of $S(G)$ on $H$ and $C^*$-algebra representations of $C_p^*(G)$ on $H$.
