The reduced Hao-Ng isomorphism problem for product systems
Abstract
We prove that the reduced Hao-Ng isomorphism problem has an affirmative answer for every generalised gauge action of a locally compact Hausdorff group on a product system over a unital subsemigroup of a discrete group, without any assumptions on the product system or the subsemigroup. We show that the Fock C*-algebra of the induced product system is canonically isomorphic to the reduced crossed product of the Fock C*-algebra, by identifying the Fock space of the induced product system with the reduced crossed product of the Fock space. This also yields the corresponding completely isometric isomorphism for the tensor algebras. Using the representations of the fixed point algebra that detect Sehnem's strong covariance relations, we show that the canonical representation of the induced product system in the reduced crossed product of the reduced strong covariant C*-algebra is strong covariant.
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BibTeX
@misc{paraskevas2026reduced,
title = {{The reduced Hao-Ng isomorphism problem for product systems}},
author = {Ioannis Apollon Paraskevas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.17824},
eprint = {2607.17824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.17824},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The reduced Hao-Ng isomorphism problem for product systems
AU - Ioannis Apollon Paraskevas
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2607.17824
UR - https://arxiv.org/abs/2607.17824
AB - We prove that the reduced Hao-Ng isomorphism problem has an affirmative answer for every generalised gauge action of a locally compact Hausdorff group on a product system over a unital subsemigroup of a discrete group, without any assumptions on the product system or the subsemigroup. We show that the Fock C*-algebra of the induced product system is canonically isomorphic to the reduced crossed product of the Fock C*-algebra, by identifying the Fock space of the induced product system with the reduced crossed product of the Fock space. This also yields the corresponding completely isometric isomorphism for the tensor algebras. Using the representations of the fixed point algebra that detect Sehnem's strong covariance relations, we show that the canonical representation of the induced product system in the reduced crossed product of the reduced strong covariant C*-algebra is strong covariant.
ER -