Abstract
Given a discrete abelian group G and σ∈Ğ, the C*-crossed product\(G x_{\tilde \sigma } C (T)\) for the G-action\(\tilde \sigma _S (f) = f(< \overline {s,\sigma } > \cdot )\) on C(T) generalizes rotation C*-algebras studied by Høegh-Krohn, Skjelbred [9], Pimsner,Voiculescu [16], Riedel [18], Rieffel [19] and others. We treat\(G x_{\tilde \sigma } C (T)\) in the frame of a larger class of C*-algebras, each defined by generators with a σ-twisted commutation property. A description of such algebras as twisted C*-crossed products leads to centre, ideal lattice, primitive ideal space, tracial functionals, a characterization of simplicity and a classification under liminarity conditions. The subclass corresponding to faithful characters is classified up to isomorphism.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albeverio, S., Høegh-Krohn, R.: Ergodic actions by compact groups on C*-algebras. Math. Z.174, 1–17 (1980)
Bunce, J.: Characterizations of amenable and strongly amenable C*-algebras. Pac. J. Math.43, 563–572 (1972)
Connes, A.: On the cohomology of operator algebras. J. Funct. Anal.28, 248–253 (1978)
De Brabanter, M.: Decomposition theorems for certain C*-crossed products. Math. Proc. Camb. Philos. Soc., to appear
De Brabanter, M.: The classification of rational rotation C*-algebras. Preprint Leuven (1983)
Ghatage, P.G.: C*-algebras generated by weighted shifts. Indiana Univ. Math. J.28, 1007–1012 (1979)
Ghatage, P.G., Phillips, W.J.: C*-algebras generated by weighted shifts II. Indiana Univ. Math. J.30, 539–546 (1981)
Henrard, G.: Duality and a fixed point theorem for almost periodic C*-crossed products. Preprint Leuven (1983)
Høegh-Krohn, R., Skjelbred, T.: Classification of C*-algebras admitting ergodic actions of the two-dimensional torus. J. Reine Angew. Math.328, 1–8 (1981)
Johnson, B.E.: Cohomology in Banach algebras. Mem.Amer. Math. Soc.127; AMS, Providence R.I. (1972)
Kishimoto, A., Takai, H.: Some remarks on C*-dynamical systems with a compact abelian group. Publ. Res. Inst. Mat. Sci.14, 383–397 (1978)
Landstad, M.B.: Duality theory for covariant systems. Trans. Amer. Math. Soc.248, 223–267 (1979)
Olesen, D., Pedersen, G.K., Takesaki, M.: Ergodic actions of compact abelian groups. J. Oper. Theory3, 237–269 (1980)
Pedersen, G.K.: The linear span of projections in simple C*-algebras. J. Oper. Theory4, 289–296 (1980)
Pedersen, G.K.: C*-algebras and their automorphism groups. London Math. Soc. Monographs 14, London-New York: Academic Press 1979
Pimsner, M., Voiculescu, D.: Imbedding the irrational rotation C*-algebra into an AF-algebra. J. Oper. Theory4, 199–208 (1980)
Pontryagin, L.S.: Topological groups. 2nd Ed. London-New York: Gordon and Breach 1966
Riedel, N.: Classification of the C*-algebras associated with minimal rotations. Pac. J. Math.101, 153–161 (1982)
Rieffel, M.A.: C*-algebras associated with irrational rotations. Pac. J.Math.93, 415–429 (1981)
Rosenberg, J.: Amenability of crossed products of C*-algebras. Commun. Math. Phys.57, 187–191 (1977)
Sutherland, C.E.: Cohomology and extensions of von Neumann algebras, II. Publ. Res. Inst. Mat. Sci.16, 135–174 (1980)
Zeller-Meier, G.: Produits croisés d'une C*-algèbre par un groupe d'automorphismes. J. Math. Pures Appl. IX Sér.47, 101–239 (1968)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
De Brabanter, M., Zettl, H.H. C*-algebras associated with rotation groups and characters. Manuscripta Math 47, 153–174 (1984). https://doi.org/10.1007/BF01174591
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01174591