Decomposing the $C^*$-algebras of groupoid extensions
HTML articles powered by AMS MathViewer
- by Jonathan H. Brown and Astrid an Huef PDF
- Proc. Amer. Math. Soc. 142 (2014), 1261-1274 Request permission
Abstract:
We decompose the full and reduced $C^*$-algebras of an extension of a groupoid by the circle into a direct sum of twisted groupoid $C^*$-algebras.References
- C. Anantharaman-Delaroche and J. Renault, Amenable groupoids, Monographies de L’Enseignement Mathématique [Monographs of L’Enseignement Mathématique], vol. 36, L’Enseignement Mathématique, Geneva, 2000. With a foreword by Georges Skandalis and Appendix B by E. Germain. MR 1799683
- Jonathan Henry Brown, Proper actions of groupoids on $C^*$-algebras, J. Operator Theory 67 (2012), no. 2, 437–467. MR 2928324
- Lisa Orloff Clark, CCR and GCR groupoid $C^*$-algebras, Indiana Univ. Math. J. 56 (2007), no. 5, 2087–2110. MR 2359724, DOI 10.1512/iumj.2007.56.2955
- Lisa Orloff Clark and Astrid an Huef, The representation theory of $C^*$-algebras associated to groupoids, Math. Proc. Cambridge Phil. Soc. 153 (2012), 167–191.
- Shaun Disney and Iain Raeburn, Homogeneous $C^\ast$-algebras whose spectra are tori, J. Austral. Math. Soc. Ser. A 38 (1985), no. 1, 9–39. MR 765447
- J. M. G. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472–476. MR 139135, DOI 10.1090/S0002-9939-1962-0139135-6
- Geoff Goehle, Groupoid crossed products, ProQuest LLC, Ann Arbor, MI, 2009. Thesis (Ph.D.)–Dartmouth College. MR 2941279
- Elliot C. Gootman, The type of some $C^{\ast }$ and $W^{\ast }$-algebras associated with transformation groups, Pacific J. Math. 48 (1973), 93–106. MR 335681
- Alexander Kumjian, On $C^\ast$-diagonals, Canad. J. Math. 38 (1986), no. 4, 969–1008. MR 854149, DOI 10.4153/CJM-1986-048-0
- Paul S. Muhly, Jean N. Renault, and Dana P. Williams, Continuous-trace groupoid $C^\ast$-algebras. III, Trans. Amer. Math. Soc. 348 (1996), no. 9, 3621–3641. MR 1348867, DOI 10.1090/S0002-9947-96-01610-8
- Paul S. Muhly and Baruch Solel, Subalgebras of groupoid $C^*$-algebras, J. Reine Angew. Math. 402 (1989), 41–75. MR 1022793, DOI 10.1515/crll.1989.402.41
- Paul S. Muhly and Dana P. Williams, Continuous trace groupoid $C^*$-algebras, Math. Scand. 66 (1990), no. 2, 231–241. MR 1075140, DOI 10.7146/math.scand.a-12307
- Paul S. Muhly and Dana P. Williams, Continuous trace groupoid $C^*$-algebras. II, Math. Scand. 70 (1992), no. 1, 127–145. MR 1174207, DOI 10.7146/math.scand.a-12390
- Milan Pahor, The structure of certain group $C^*$-algebras, Bull. Austral. Math. Soc. 47 (1993), no. 1, 169–174. MR 1201434, DOI 10.1017/S0004972700012375
- Gert K. Pedersen, $C^{\ast }$-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1979. MR 548006
- Jean Renault, A groupoid approach to $C^{\ast }$-algebras, Lecture Notes in Mathematics, vol. 793, Springer, Berlin, 1980. MR 584266
- Jean Renault, Représentation des produits croisés d’algèbres de groupoïdes, J. Operator Theory 18 (1987), no. 1, 67–97 (French). MR 912813
- Jean Renault, Cartan subalgebras in $C^*$-algebras, Irish Math. Soc. Bull. 61 (2008), 29–63. MR 2460017
- Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace $C^*$-algebras, Mathematical Surveys and Monographs, vol. 60, American Mathematical Society, Providence, RI, 1998. MR 1634408, DOI 10.1090/surv/060
- Dana P. Williams, The structure of crossed products by smooth actions, J. Austral. Math. Soc. Ser. A 47 (1989), no. 2, 226–235. MR 1008836
- Dana P. Williams, Crossed products of $C{^\ast }$-algebras, Mathematical Surveys and Monographs, vol. 134, American Mathematical Society, Providence, RI, 2007. MR 2288954, DOI 10.1090/surv/134
Additional Information
- Jonathan H. Brown
- Affiliation: Department of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand
- Address at time of publication: Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, Kansas 66506-2602
- MR Author ID: 982203
- Email: jbrown@maths.otago.ac.nz, brownjh@math.ksu.edu
- Astrid an Huef
- Affiliation: Department of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand
- MR Author ID: 620419
- Email: astrid@maths.otago.ac.nz
- Received by editor(s): April 28, 2011
- Received by editor(s) in revised form: October 8, 2011, and May 6, 2012
- Published electronically: January 13, 2014
- Additional Notes: The authors thank Iain Raeburn and Dana Williams for helpful discussions
- Communicated by: Marius Junge
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 1261-1274
- MSC (2010): Primary 46L55, 46L05
- DOI: https://doi.org/10.1090/S0002-9939-2014-11492-4
- MathSciNet review: 3162248