$\mathbb{Z}^{d}$生成子半群上乘积系统的本质表示
An essential representation for a product system over a finitely generated subsemigroup of $\mathbb{Z}^{d}$
摘要：
设$S \subset \mathbb{Z}^{d}$是一个非线性生成子半群.设$E$是$S$上的乘积系统。证明了存在无穷维可分希尔伯特空间$\mathcal{H}$和$B(\mathcal{H})$的单位正规$*$ -自同态半群$α:=\{α_x\}_{x \in S}$，使得$E$同构于与$α$相关的乘积系统.
英文摘要：
Let $S \subset \mathbb{Z}^{d}$ be a finitely generated subsemigroup. Let $E$ be a product system over $S$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $α:=\{α_x\}_{x \in S}$ of unital normal $*$-endomorphisms of $B(\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $α$.
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