An essential representation for a product system over a finitely generated subsemigroup of $\mathbb{Z}^{d}$

S.P.Murugan; S.Sundar

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An essential representation for a product system over a finitely generated subsemigroup of mathbb{Z}^(d)

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arxiv 1709.08152 v2 pith:5YOJTDA2 submitted 2017-09-24 math.OA

An essential representation for a product system over a finitely generated subsemigroup of mathbb{Z}^(d)

S.P.Murugan , S.Sundar This is my paper

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keywords alphaproductsystemfinitelygeneratedmathbbmathcalsubsemigroup

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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 $\alpha:=\{\alpha_x\}_{x \in S}$ of unital normal $*$-endomorphisms of $B(\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $\alpha$.

An essential representation for a product system over a finitely generated subsemigroup of mathbb{Z}^(d)

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