An essential representation for a product system over a finitely generated subsemigroup of Zᵈ

الأصل · EN

Let S ⊂ Zᵈ be a finitely generated subsemigroup. Let E be a product system over S. We show that there exists an infinite dimensional separable Hilbert space H and a semigroup α:={αₓ}ₓ ∈ ₛ of unital normal *-endomorphisms of B(H) such that E is isomorphic to the product system associated to α.