C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems

A cosystem consists of a possibly nonselfadoint operator algebra equipped with coaction by discrete group. We introduce the concept C*-envelope for cosystem; roughly speaking, this is smallest C*-algebraic that contains an equivariant completely isometric copy original one. show always exists and we explain how it relates to usual C*-envelope. then compactly aligned product systems over group-embeddable right LCM semigroups, co-universal, in sense Carlsen, Larsen, Sims Vittadello, Fock tensor its natural coaction. This yields existence co-universal C*-algebra, generalizing previous results Dor-On Katsoulis. also realize as reduced cross sectional Fell bundle introduced Sehnem, which, under mild assumption normality, identify quotient image Sehnem's strong covariance ideal. In another application, obtain Hao-Ng isomorphism theorem algebras.