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Representations of triangular subalgebras of groupoid C*-algebras

Part of: Selfadjoint operator algebras Groupoids Topological (rings and) algebras with an involution

Published online by Cambridge University Press:  09 April 2009

Paul S. Muhly  and
Baruch Solel
Paul S. Muhly
Affiliation:
Department of Mathematics University of IowaIowa City, IA 52242, USA
Baruch Solel
Affiliation:
Department of Mathematics Technion-Israel Institute of Technology Haifa 32000, Israel
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Abstract

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We investigate the invariant subspace structure of subalgebras of groupoid C*-algebras that are determined by automorphism groups implemented by cocycles on the groupoids. The invariant subspace structure is intimately tied to the asymptotic behavior of the cocycle.

MSC classification

Secondary: 46K50: Nonselfadjoint (sub)algebras in algebras with involution 46L40: Automorphisms 20L99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 3 , December 1996 , pp. 289 - 321
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Arveson, W. B., ‘On groups of automorphisms of operator algebras’, J. Funct. Anal. 15 (1974), 217–243.CrossRefGoogle Scholar
[2]Arveson, W. B., ‘Subalgebras of C*-algebras I’, Acta Math. 123 (1969), 141–224.CrossRefGoogle Scholar
[3]Arveson, W. B., ‘Subalgebras of C*-algebras II’, Acta Math. 128 (1972), 271–308.CrossRefGoogle Scholar
[4]Arveson, W. B. and Josephson, K., ‘Operator algebras and measure preserving automorphisms II’, J. Funct. Anal. 4 (1969), 100–134.CrossRefGoogle Scholar
[5]Doubilet, P., Rota, G. -C., and Stanley, R., ‘On the foundations of combinatorial theory (VI): The idea of a generating function’, in: Proc. Sixth Berkeley Symposium in Math., Stat. and Prob., Vol. II (1971), pp. 267–318.Google Scholar
[6]Feldman, J. and Moore, C., ‘Ergodic equivalence relations, cohomology and von Neumann algebras I’, Trans. Amer. Math. Soc. 234 (1977), 289–324.CrossRefGoogle Scholar
[7]Feldman, J. and Moore, C., ‘Ergodic equivalence relations, cohomology and von Neumann algebras II’, Trans. Amer. Math. Soc. 234 (1977), 325–359.CrossRefGoogle Scholar
[8]Hopenwasser, A. and Power, S. C., ‘Classification of limits of triangular matrix algebras’, Proc. Edingburgh Math. Soc. 36 (1992), 107–121.CrossRefGoogle Scholar
[9]Kawamura, S. and Tomiyama, J., ‘On subdiagonal algebras associated with flows in operator algebras’, J. Math. Soc. Japan 29 (1977), 73–90.CrossRefGoogle Scholar
[10]Kumjian, A., ‘On C*-diagonals’, Canad. J. Math. 38 (1986), 969–1008.CrossRefGoogle Scholar
[11]Loebl, R. I. and Muhly, P. S., ‘Analyticity and flows in von Neumann algebras’, J. Funct. Anal. 29 (1978), 214–252.CrossRefGoogle Scholar
[12]Muhly, P. S., Qiu, C. and Solel, B., ‘Coordinates, nuclearity and spectral subspace in operator algebra’, J. Operator Theory 26 (1991), 313–332.Google Scholar
[13]Muhly, P. S., Saito, K.-S. and Solel, B., ‘Coordinates for triangular operator algebras’, Ann. of Math. 127 (1988), 245–278.CrossRefGoogle Scholar
[14]Muhly, P. S., Saito, K.-S. and Solel, B., ‘Coordinates for triangular operator algebras II’, Pacific J. Math. 137 (1989), 335–369.CrossRefGoogle Scholar
[15]Muhly, P. S. and Solel, B., ‘On triangular subalgebras of groupoid C*-algebras’, Israel. J. Math. 71 (1990), 257–273.CrossRefGoogle Scholar
[16]Muhly, P. S., and Solel, B., ‘Dilations and commutant lifting for subalgebras of groupoid C*-algebras’, Internat. J. Math. 5 (1994), 87–123.CrossRefGoogle Scholar
[17]Muhly, P. S., and Solel, B., ‘Hilbert modules over operator algebras’, Mem. Amer. Math. Soc. vol. 117, #559 (1995).Google Scholar
[18]Olesen, D., ‘On spectral subspaces and their applications to automorphism groups’, Sympos. Math. 20 (1976), 253–296.Google Scholar
[19]Orr, J. L. and Peters, J. R., ‘Some representations of TAF algebras’, Pacific J. Math. 167 (1995), 129–161.CrossRefGoogle Scholar
[20]Pedersen, G. K., C*-algebras and their automorphism groups, London Math. Soc. Monograph 14, (Academic Press, New York, 1979).Google Scholar
[21]Peters, J. R., Poon, Y. T. and Wagner, B. H., ‘Triangular AF algebras’, J. Operator Theory 23 (1990), 81–114.Google Scholar
[22]Peters, J. R., Poon, Y. T. and Wagner, B. H., ‘Analytic TAF algebras’, Canad. J. Math. 45 (1993), 1009–1031.CrossRefGoogle Scholar
[23]Peters, J. R. and Wagner, B. H., ‘Triangular AF algebras and nest subalgebras of UHF algebras’, J. Operator Theory 25 (1991), 79–124.Google Scholar
[24]Power, S. C., Limit algebras: an introduction to subalgebras of C*-algebras, Pitman Res. Notes Math. Ser. 278 (Longman Sci. and Tech., 1992).Google Scholar
[25]Ramsay, A., ‘Nontransitive quasi-orbits in Mackey's analysis of group extensions’, Acta Math. 137 (1976), 17–48.CrossRefGoogle Scholar
[26]Renault, J., A groupoid approach to C*-algebras, Lecture Notes in Math. 793 (Springer, Berlin, 1980).CrossRefGoogle Scholar
[27]Renault, J., Représentation des produits croisés d'algèbres de groupoîdes, J. Operator Theory 18 (1987), 67–97.Google Scholar
[28]Schmidt, K., Cocycles on ergodic transformation groups, McMillan Lect. in Math. 1 (The Macmillan Company of India, 1977).Google Scholar
[29]Solel, B., Applications of the asymptotic range to analytic subalgebras of groupoid C*-algebras, Ergodic Theory Dynamical Systems 12 (1992), 341–358.CrossRefGoogle Scholar