Abstract
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 \(\alpha \).
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Acknowledgements
The authors would like to thank Prof. Partha Sarathi Chakraborty for his geometric insight which helped them in proving Lemma 3.8.
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Communicating Editor: B V Rajarama Bhat
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Murugan, S.P., Sundar, S. An essential representation for a product system over a finitely generated subsemigroup of \(\pmb {{\mathbb {Z}}}^{{\varvec{d}}}\). Proc Math Sci 129, 17 (2019). https://doi.org/10.1007/s12044-018-0456-6
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DOI: https://doi.org/10.1007/s12044-018-0456-6