In the present article, we provide several constructions of C*-dynamical systems
with a compact group
in terms of Cuntz–Pimsner algebras. These systems have a minimal relative commutant of the fixed-point algebra
in
, i.e.
, where
is the center of
, which is assumed to be non-trivial. In addition, we show in our models that the group action
has full spectrum, i.e. any unitary irreducible representation of
is carried by a
-invariant Hilbert space within
.
First, we give several constructions of minimal C*-dynamical systems in terms of a single Cuntz–Pimsner algebra
associated to a suitable
-bimodule ℌ. These examples are labelled by the action of a discrete Abelian group ℭ (which we call the chain group) on
and by the choice of a suitable class of finite dimensional representations of
. Second, we present a more elaborate contruction, where now the C*-algebra
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
, N ≥ 2.
