Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T11:57:49.371Z Has data issue: false hasContentIssue false
  • English
  • Français

ON GRADED $C^{\ast }$-ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  04 October 2017

IAIN RAEBURN Open the ORCID record for IAIN RAEBURN [Opens in a new window]
IAIN RAEBURN*
Affiliation:
Department of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that every topological grading of a $C^{\ast }$-algebra by a discrete abelian group is implemented by an action of the compact dual group.

Keywords

gradingFell bundlegraph algebra

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 1 , February 2018 , pp. 127 - 132
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Abrams, G. and Aranda Pino, G., ‘The Leavitt path algebra of a graph’, J. Algebra 293 (2005), 319–334.Google Scholar
Abrams, G., Ara, P. and Siles Molina, M., Leavitt Path Algebras: A Primer and Handbook , to appear, available at academics.uccs.edu/gabrams.CrossRefGoogle Scholar
Exel, R., ‘Amenability for Fell bundles’, J. reine angew. Math. 492 (1997), 41–73.Google Scholar
Exel, R., Partial Dynamical Systems, Fell Bundles and Applications , to appear, arXiv:1511.04565.Google Scholar
Fell, J. M. G. and Doran, R. S., Representations of ∗ -Algebras, Locally Compact Groups, and Banach ∗ -Algebraic Bundles, Pure and Applied Mathematics, 125 and 126 (Academic Press, San Diego, 1988).Google Scholar
Kumjian, A. and Pask, D., ‘Higher rank graph C ∗ -algebras’, New York J. Math. 6 (2000), 1–20.Google Scholar
Kumjian, A., Pask, D. and Sims, A., ‘Homology for higher-rank graphs and twisted C ∗ -algebras’, J. Funct. Anal. 263 (2012), 1539–1574.CrossRefGoogle Scholar
Kumjian, A., Pask, D. and Sims, A., ‘On twisted higher-rank graph C ∗ -algebras’, Trans. Amer. Math. Soc. 367 (2015), 5177–5216.CrossRefGoogle Scholar
Landstad, M. B., Phillips, J., Raeburn, I. and Sutherland, C. E., ‘Representations of crossed products by coactions and principal bundles’, Trans. Amer. Math. Soc. 299 (1987), 747–784.Google Scholar
Quigg, J. C., ‘Discrete coactions and C ∗ -algebraic bundles’, J. Aust. Math. Soc. 60 (1996), 204–221.CrossRefGoogle Scholar
Raeburn, I., Graph Algebras, CBMS Regional Conference Series in Mathematics, 103 (American Mathematical Society, Providence, RI, 2005).CrossRefGoogle Scholar
Raeburn, I., Graph Algebras: Bridging the Gap between Algebra and Analysis (eds. Aranda Pino, G., Domenesc Perera, F. and Siles Molina, M.) (University of Malaga, 2007), Ch. 1, available online at http://webpersonal.uma.es/∼MSILESM/Pub_BST_files/APS_Edts.pdf.Google Scholar
Raeburn, I., ‘Deformations of Fell bundles and twisted graph algebras’, Math. Proc. Cambridge Philos. Soc. 161 (2016), 535–558.Google Scholar
Raeburn, I. and Williams, D. P., Morita Equivalence and Continuous-Trace C ∗ -Algebras, Mathematical Surveys and Monographs, 60 (American Mathematical Society, Providence, RI, 1998).CrossRefGoogle Scholar