On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions

Evgenios T. A. Kakariadis; Ioannis Apollon Paraskevas

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arXiv · 2403.19764

On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions

Evgenios T. A. Kakariadis·Ioannis Apollon Paraskevas

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Abstract

We provide a characterisation of equivariant Fock covariant injective representations for product systems. We show that this characterisation coincides with Nica covariance for compactly aligned product systems over right LCM semigroups of Kwa\'{s}niewski and Larsen, and with the Toeplitz representations of a discrete monoid of Laca and Sehnem. By combining with the framework established by Katsoulis and Ramsey, we resolve the reduced Hao-Ng isomorphism problem for generalised gauge actions by discrete groups.

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Evgenios T. A. Kakariadis, Ioannis Apollon Paraskevas. 2024-03-28. On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions. https://arxiv.org/abs/2403.19764

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