# Realization of Minimal C* - Dynamical Systems in Terms of Cuntz-Pimsner Algebras Articles

• June 2009

• 751

• 790

• 6

• 20

• 0129-167X

• 1793-6519

### abstract

• In the present article, we provide several constructions of C*-dynamical systems (F,G,\beta) with a compact group G in terms of Cuntz&-Pimsner algebras. These systems have a minimal relative commutant of the fixed-point algebra A := F\sp G in F, i.e. A' \cap F = Z, where Z is the center of A, which is assumed to be non-trivial. In addition, we show in our models that the group action beta: G -> AutF has full spectrum, i.e. any unitary irreducible representation of G is carried by a beta_G-invariant Hilbert space within F.First, we give several constructions of minimal C*-dynamical systems in terms of a single Cuntz&-Pimsner algebra F = O_ℌ associated to a suitable Z-bimodule ℌ. These examples are labelled by the action of a discrete Abelian group ℭ (which we call the chain group) on Z and by the choice of a suitable class of finite dimensional representations of G. Second, we present a more elaborate contruction, where now the C*-algebra F is generated by a family of Cuntz&-Pimsner algebras. Here, the product of the elements in different algebras is twisted by the chain group action. We specify the various constructions of C*-dynamical systems for the group G = SU(N), N ≥ 2.