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Applications of the asymptotic range to analytic subalgebras of groupoid C*-algebras

Published online by Cambridge University Press:  19 September 2008

Baruch Solel
Baruch Solel
Affiliation:
Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel
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Abstract

For a 1-cocycle c on a principal r-discrete groupoid G, that vanishes only on the unit space of G, we show that the asymptotic range of c, , is an invariant for the total order c−1([0, ∞]). It follows that is also an invariant (with respect to isometric isomorphisms) of the triangular analytic algebra supported on c−1([0, ∞]). We also prove that if and only if the analytic algebra has a certain maximality property.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 2 , June 1992 , pp. 341 - 358
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

[D]Davidson, K.. Nest algebras. Potman Research Notes in Math. 191 (Longman Scientific and Technical, 1988).Google Scholar
[FM]Feldman, J. and Moore, C. C.. Ergodic equivalence relations, cohomology, and von Neumann algebras I. Trans. Amer. Math. Soc. 234 (1977), 289–324.CrossRefGoogle Scholar
[K]Kawahigashi, Y.. One parameter automorphism groups of the hyperfinite type II1 factor. J. Operator Theory (to appear).Google Scholar
[KT]Kawamura, S. & Tomiyama, J.. On subdiagonal algebras associated with flows in operator algebras. J. Math. Soc. Japan 29 (1977), 73–90.Google Scholar
[LM]Loebl, R. I. & Muhly, P. S.. Analyticity and flows in von Neumann algebras. J. Funct. Anal. 29 (1978), 214–252.CrossRefGoogle Scholar
[MQS]Muhly, P. S., Qiu, C. & Solel, B.. Intrinsic Isomorphism invariants for some triangular operator algebras. Self adjoint and non-self adjoint operator algebras.Google Scholar
[MS1]Muhly, P. S. & Solel, B.. Subalgebras of groupoid C*-algebras. J. Reine und Angew. Math. 402 (1989), 41–75.Google Scholar
[MS2]Muhly, P. S. & Solel, B.. On triangular subalgebras of groupoid C*-algebras. Israel J. Math. 71 (1990), 257–274.CrossRefGoogle Scholar
[OP]Olesen, D. & Pedersen, G. K.. Applications of the Connes spectrum to c*-dynamical systems. J. Fund. Anal. 30 (1978), 179–197.CrossRefGoogle Scholar
[PPW]Peters, J., Poon, Y. & Wagner, B.. Triangular AF algebras. J. Operator Theory 23 (1990), 81–114.Google Scholar
[PW]Peters, J. & Wagner, B.. Triangular AF algebras and nest subalgebras of UHF algebras. Preprint.Google Scholar
[R]Renault, J.. A groupoid approach to c*-algebras. Springer Lecture Notes in Mathematics 793 (Springer: Berlin-Heidelberg-New York, 1980).Google Scholar
[S1]Solel, B.. Analytic operator algebras.Google Scholar
[S2]Solel, B.. Maximality of analytic operator algebras. Israel J. Math. 62 (1988), 63–89.CrossRefGoogle Scholar
[SV]Solel, B. & Ventura, B.. Analytic triangular AF algebras. In preparation.Google Scholar
[T]Thelwall, M. A.. Maximal triangular subalgebras of AF algebras. Preprint.Google Scholar
[V1]Ventura, B.. A note on subdiagonality for triangular AF algebras. Proc. Amer. Math. Soc.Google Scholar
[V2]Ventura, B.. Strongly maximal triangular UHF algebras.Google Scholar