PROJECTIVE COVARIANT REPRESENTATIONS OF LOCALLY C*-DYNAMICAL SYSTEMS

Abstract

As a generalization of covariant completely positive maps, we consider (projective) covariant a-completely positive maps between locally C*-algebras. We first study (projective) covariant J-representations of locally C*-algebras on Krein modules over locally C*-algebras. Secondly, we construct a covariant KS-GNS type representation associated with a covariant alpha-completely positive map on a locally C*-algebra, and then study extensions to a locally C*-crossed product of alpha-completely positive maps on a locally C*-algebra. The results provide (projective) covariant representations of a locally C*-crossed product on a Krein module over a locally C*-algebra.