Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-06T01:19:20.341Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytic Taf Algebras

Published online by Cambridge University Press:  20 November 2018

J. R. Peters ,
Y. T. Poon  and
B. H. Wagner
J. R. Peters
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
Y. T. Poon
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
B. H. Wagner
Affiliation:
Department of Mathematics Iowa State University Ames, Iowa 50011 U.S.A.
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.

A strongly maximal triangular AF algebra which is defined by a realvalued cocycle is said to be analytic. Formulas for generic cocycles are given separately for both the integer-valued case and the real-valued coboundary case, and also for certain nest algebras. In the case of an integer-valued cocycle, there is an associated partial homeomorphismof the maximal ideal space of the diagonal. If the partial homeomorphism extends to a homeomorphism, then the algebra embeds in a crossed product. This occurs for a large class of subalgebras of UHF algebras, but an example shows that this does not always occur. An example is given of a triangular AF algebra which is analytic via a coboundary but is not a nest algebra; also, it is shown that a nest algebra need not be analytic

Keywords

46H2046L05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 1009 - 1031
Copyright
Copyright © Canadian Mathematical Society 1993

References

[Ba] Baker, R.L., Triangular UHF algebras, J. Func. Anal. 91(1990), 182–212.Google Scholar
[Br] Bratteli, O., Inductive limits of finite dimensional C*-algebras, Trans. Amer. Math. Soc. 171(1972), 195–234.Google Scholar
[G] Glimm, J., On a certain class of operator algebras, Trans. Amer. Math. Soc. 95(1960), 318–340.Google Scholar
[HP] Hopenwasser, A. and Power, S.C., Classification of limits of triangular matrix algebras, preprint.Google Scholar
[MSI] Muhly, P.S. and Solel, B., Subalgebras of groupoid C -algebras, J. reine angew. Math. 402(1989), 41–75.Google Scholar
[MS2] Muhly, P.S., On triangular subalgebras of’ group oid C-algebras, Israel J. Math. 71(1990), 257–273.Google Scholar
[MSS1] Muhly, P.S. Saito, K.-S. and B. Solel, Coordinates for triangular operator algebras, Ann. Math. 127(1988), 245–278.Google Scholar
[MSS2] Muhly, P.S., Coordinates for triangular operator algebras II, Pacific J. Math. 137(1989), 335–369.Google Scholar
[PPW] Peters, J.R., Poon, Y.T. and Wagner, B.H., Triangular AF algebras, J. Operator Theory 23(1990), 81–114.Google Scholar
[PW] Peters, J.R. andWagner, B.H., Triangular AF algebras and nest subalgebras of'UHF algebras, J. Operator Theory to appear.Google Scholar
[PWo] Peters, J.R. and Wogen, W.R., Reflexive subalgebras of AF algebras, preprint.Google Scholar
[Pol] Poon, Y T., AF subalgebras of certain crossed products, Rocky Mountain J. Math. 20(1990), 527–537.Google Scholar
[Po2] Poon, Y T., Maximal triangular subalgebras need not be closed, Proc. Amer. Math. Soc. 111(1991), 475- 479.Google Scholar
[Po3] Poon, Y T., A complete isomorphism invariant for certain triangularUHF subalgebras, J. Operator Theory to appear.Google Scholar
[Prl] Power, S.C., On ideals of nest subalgebras of C*-algebras, Proc. London Math. Soc. (3) 50(1985), 314–332.Google Scholar
[Pr2] Power, S.C., Classifications of tensor products of triangular operator algebras, Proc. London Math. Soc. (3) 61(1990), 571–614.Google Scholar
[Pr3] Power, S.C., The classification of triangular subalgebras of AFC* -algebras, Bull. London Math. Soc. 72 (1990), 269–272.Google Scholar
[Pu] Putnam, I., The C* -algebras associated with minimal homeomorphisms of the Cantor set, Pacific J. Math. 136(1989), 329–353.Google Scholar
[R] Renault, J., A groupoidapproach to C* -algebras, Springer Lect. Notes in Math. 7931980.Google Scholar
[S] Solel, B., Applications of the asymptotic range to analytic subalgebras of groupoid C* -algebras, J. Ergodic Theory and Dynamical Systems, to appear.Google Scholar
[SVe] Sole!, B. and Ventura, B., Analyticity in triangularUHF algebras, preprint.Google Scholar
[SV] Stratila, S. and Voiculescu, D., Representations of AF algebras and of the group U(oo), Springer Lect. Notes in Math. 486(1975).Google Scholar
[T] Thelwall, M., Maximal triangular subalgebras of AF algebras, J. Operator Theory, to appear.Google Scholar
[VI] Ventura, B., A note on subdiagonality for triangular AF algebras, Proc. Amer. Math. Soc. 110(1990), 775–779.Google Scholar
[V2] Ventura, B., Strongly maximal triangular AF algebras, International J. Math., (5) 2(1991), 567–598.Google Scholar