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On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions
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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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The Hao-Ng isomorphism theorem for reduced crossed products
For any C*-correspondence with a generalized gauge action by a locally compact Hausdorff group, the Cuntz-Pimsner algebra of the reduced crossed product is canonically isomorphic to the reduced crossed product of the ...
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