2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62988The $C^*$-algebra associated with the twisted CCR constructed by W. Pusz and S.L. Woronowicz is considered. It is proved that the $C^*$-algebras corresponding to different values of parameter $0<=μ<1$ are isomorphic. It is proved that Fock representation is faithful on both *-algebra and $C^*$-algebra levels.11 pagesOperator AlgebrasRepresentation Theory46L55, 46L65, 81S05, 81T05text