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

Part of: Linear spaces and algebras of operators Selfadjoint operator algebras

Published online by Cambridge University Press:  28 April 2025

Evgenios T. A. Kakariadis  and
Ioannis Apollon Paraskevas
Evgenios T. A. Kakariadis
Affiliation:
School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK ([email protected])
Ioannis Apollon Paraskevas*
Affiliation:
Department of Mathematics, National and Kapodistrian University of Athens, Panepistimiopolis, Athens, 157 84, Greece ([email protected]) (corresponding author)
*
*Corresponding author.
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Abstract

We provide a characterization of equivariant Fock covariant injective representations for product systems. We show that this characterization coincides with Nica covariance for compactly aligned product systems over right least common multiple semigroups of Kwaśniewski 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 generalized gauge actions by discrete groups.

Keywords

product systemsFock spacecrossed products of operator algebras

MSC classification

Primary: 46L08: $C^*$-modules
Secondary: 47L55: Representations of (nonselfadjoint) operator algebras 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 53
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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