Citation:
International Journal of Mathematics (IJM), 2009, vol. 20, n. 6, p. 751-790

ISSN:
0129-167X

DOI:
10.1142/S0129167X09005522

Sponsor:
We are grateful to the DFG-Graduiertenkolleg "Hierarchie und Symmetrie
in mathematischen Modellen" for supporting a visit of E.V. to the RWTH-Aachen.

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 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 β: G -> AutF has full spectrum, i.e. any unitary irreducible representation of G is carried by a β_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 grouFirst, 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.[+][-]

Description:

40 pages, no figures.-- MSC2000 codes: 46L08, 47L80, 22D25.-- ArXiv pre-print available at: http://arxiv.org/abs/math/0702775

Dedicated to Klaus Fredenhagen on his 60th birthday.