Speaker
Ioannis Apollon Paraskevas, University of Athens
Abstract
\(C^*\)-algebras and nonselfadjoint algebras associated to product systems capture a vast number of constructions arising from discrete structures, such as semigroups, (topological) graphs and dynamical systems. In this talk, 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 Kwasniewski 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.