Hostname: page-component-5447f9dfdb-kxt6s Total loading time: 0 Render date: 2025-07-30T01:19:51.893Z Has data issue: false hasContentIssue false
  • English
  • Français

Classification of limits of triangular matrix algebras

Published online by Cambridge University Press:  20 January 2009

A. Hopenwasser  and
S. C. Power
A. Hopenwasser
Affiliation:
Department of MathematicsUniversity of AlabamaTuscaloosa, AL 35487, USA
S. C. Power
Affiliation:
Department of MathematicsUniversity of LancasterLancaster LA1 4YL, England
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.

Let Tn be the operator algebra of upper triangular n × n complex matrices. Three families of limit algebras of the form lim (Tnk) are classified up to isometric algebra isomorphism: (i) the limit algebras arising when the embeddings Tnk→Tnk+1, are alternately of standard and refinement type; (ii) limit algebras associated with refinement embeddings with a single column twist; (iii) limit algebras determined by certain homogeneous embeddings. The last family is related to certain fractal like subsets of the unit square.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 1 , February 1993 , pp. 107 - 121
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Baker, R. L., Triangular UHF algebras, J. Funct. Anal. 91 (1990), 182–212.CrossRefGoogle Scholar
2.Davidson, K. R. and Power, S. C., Isometric automorphisms and homology for non-self-adjoint operator algebras, Quart. J. Math. 42 (1991), 271–292.CrossRefGoogle Scholar
3.Glimm, J., On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340.Google Scholar
4.Muhly, P. S. and Solel, B., On triangular subalgebras of groupoid C*-algebras, preprint 1989.CrossRefGoogle Scholar
5.Peters, J. R., Poon, Y.-T. and Wagner, B. H., Triangular AF algebras, J. Operator Theory 23 (1990), 81–114.Google Scholar
6.Peters, J. R. and Wagner, B. H., Triangular AF algebras and nest subalgebras of UHF algebras, J. Operator Theory, to appear.Google Scholar
7.Poon, Y.-T., A complete isomorphism invariant for a class of triangular UHF algebras, J. Operator Theory, to appear.Google Scholar
8.Power, S. C., Classifications of tensor products of triangular operator algebras, Proc. London Math. Soc. 61 (1990), 571–614.Google Scholar
9.Power, S. C., The classification of triangular subalgebras of AF C*-algebras, Bull. London Math. Soc. 22 (1990), 269–272.Google Scholar
10.Power, S. C., Algebraic orders on K0 and approximately finite operator algebras, J. Operator Theory, to appear.Google Scholar
11.Stratila, S. and Voiculescu, D., Representations of AF-algebras and the group U(∞) (Lecture Notes in Mathematics, 486, Springer-Verlag, New York, 1975).CrossRefGoogle Scholar
12.Thelwall, M. A., Maximal triangular subalgebras of AF algebras, J. Operator Theory, to appear.Google Scholar
13.Thelwall, M. A., Dilation theory for subalgebras of AF algebras, J. Operator Theory, to appear.Google Scholar
14.Ventura, B. A., Strongly maximal triangular AF algebras, Internat. J. Math. 2 (1991), 567–598.CrossRefGoogle Scholar